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Expected utility maximiaation problems and stochastic control

Research Project

Project/Area Number 16340025
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka University

Principal Investigator

NAGAI HIideo  Osaka University, graduate school of engineering science, professor (70110848)

Co-Investigator(Kenkyū-buntansha) KOHATSU-HIGA Artuto  Osaka University, graduate school of engineering science, associate professor (80420412)
KOTANI Shinichi  Osaka university, graduate school ofscience, professor (10025463)
MATSUMOTO Hiroyuki  Nagoya university, graduate schcolofinformationscience, professor (00190538)
ISHII Hitoshi  Waseda University, Schealofeducationand integrated sciences, Professor (70102887)
KOIKE Shigeaki  Saitama university, graduate schcolofscience and technology, professor (90205295)
森本 宏明  愛媛大学, 大学院理工学研究科, 教授 (80166438)
関根 順  大阪大学, 大学院・基礎工学研究科, 助教授 (50314399)
Project Period (FY) 2004 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥16,740,000 (Direct Cost: ¥15,600,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2007: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2006: ¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 2005: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2004: ¥3,800,000 (Direct Cost: ¥3,800,000)
Keywordsexpected utility maximization problems / quasi-variational inequalities / transaction costs / insider trading / viscosity solutions / Hamilton-Jacobi equation / large deviation control / 線形ガウス型市場モデル / リスク鋭感的ポートフォリオ最大化 / super kernel / 密度関数推定 / モーメント問題 / 期待効用最大化 / スペクトル理論 / HJB方程式 / 最小エントロピー測度 / べき型期待効用最大化 / 最適制御 / 指数型ウィナー汎関数 / 最小エントロピー / ファクターモデル / Hamilton-Jacobi-Bellman方程式 / 確率制御 / ブラウン運動
Research Abstract

We considered expected power utility maximization problems on infinite time horizon with transaction costs. Related risk-sensitive quasi-variational inequalities were deduced. The solution of the inequality consists of the pair of constant and a function. We constructed an optimal strategy by using the function of the solution and showed the constant give the optimal value of the problem.
We studied problems on equilibrium price for insider trading and showed that there exists a stable equilibrium price for such models even though insiders affect stock prices.
We studied asymptotic behavior of the solution to a Hamilton-Jacobi equation and showed that the solution converges to the asymptotic solution on the whole. Euclidean space under relatively general assumptions.
By introducing the notion of Lp viscosity solutions we proved the existence of Lp viscosity solutions by a modified version of the Perron's method. Moreover we showed his solution turns out to be Holder continuous if the equation is uniform elliptic.
By proving differentiabilities of viscosity solutions of the obstacle problems arising from mathematical finance we constructed optimal controls.
By taking up linear Gaussian models which are incomplete market models we considered the problem minimizing a probability that growth rate of the wealth process lies below the prescribed value. The asymptotics of the probability is characterized as the dual of risk-sensitive portfolio optimization problem.

Report

(5 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (128 results)

All 2008 2007 2006 2005 2004 Other

All Journal Article (90 results) (of which Peer Reviewed: 37 results) Presentation (35 results) Book (3 results)

  • [Journal Article] PDE approach to utility maximization for market models with hidden Markov Factors2008

    • Author(s)
      Hideo NAGAI, et. al.
    • Journal Title

      "Progress in Probability" Seminar on stochastic analysis, random fields and applications, ed. Dalang, R., et. al.

      Pages: 493-506

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] An Optimal Control Variance Reduction Method for Density Estimation.2008

    • Author(s)
      A. Kebaier, et. al.
    • Journal Title

      Stochastic Processes and their applications (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Enlargement of filtrations with random times for processes with jumps2008

    • Author(s)
      Kohatsu-Higa, Arturo, et. al.
    • Journal Title

      Stochastic Processes and their applications (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Estimating Multi-dimensional density functions for random variables in Wiener space2008

    • Author(s)
      Kohatsu-Higa, Arturo, et. al.
    • Journal Title

      C. R. Acad. Sci., Paris, 346

      Pages: 335-338

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] PDE approach to utility maximization for market models with hidden Markov Factors2008

    • Author(s)
      H., Nagai, W.J., Runggaldier
    • Journal Title

      Progress in Probability" Seminar on stochastic analysis, random fields and applications, edited by Dalang, R.C., et. al. Birkhauser

      Pages: 493-506

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Estimating Multi-dimensional density functions for random variables in ' Wiener space2008

    • Author(s)
      A., Kohatsu-Higa, et. al.
    • Journal Title

      C. R. Math. Acad. Sci. Paris Vol Vol.346 5-6

      Pages: 335-338

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] PDE approach to utility maximization for market models with hidden Markov factors2008

    • Author(s)
      Hideo NAGAI,.
    • Journal Title

      ゛Progress in Probability゛ Seminar on stochastic analysis, random fields and applicatiops, ed, Dalang, R.

      Pages: 493-506

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Enlargement of filtrations with random times for processes with jumps2008

    • Author(s)
      Kohatsu-Higa Arturo,.
    • Journal Title

      Stochastic Processes and their applications (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Optimal Control Variance Reduction Method for Density Estimation.2008

    • Author(s)
      A. Kebaier
    • Journal Title

      Stochastic Processes and their applications (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on Impulse control problems with risk-sensitive criteria2007

    • Author(s)
      Hideo NAGAI
    • Journal Title

      "Stochastic Processes and Applications to Mathematical Finance", Eds. J. Akahori, et. al., World Scientific

      Pages: 219-232

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Stopping problems of certain multiplicativ functionals and optimalinvestment with transaction costs2007

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Applied Mathematics and Optimization 55

      Pages: 359-384

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Maximum principle for fully nonlinear equations via the iterated comparison function method2007

    • Author(s)
      S. Koike, et. al.
    • Journal Title

      Mathematische Annalen 339.

      Pages: 461-484

    • NAID

      120006385615

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A linear-quadratic control problem with discretionary stopping2007

    • Author(s)
      S. Koike, et. al.
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series B 8

      Pages: 261-277

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula2007

    • Author(s)
      H. Matsumoto
    • Journal Title

      Journal of Functional Analysis 244

      Pages: 565-578

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Krein' s strings with singular left boundary2007

    • Author(s)
      S. Kotani
    • Journal Title

      Report on Math. Phys 59

      Pages: 305-316

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Models for insider trading with finite utility.2007

    • Author(s)
      Kohatsu-Higa, Arturo
    • Journal Title

      Paris-Princeton Lectures on Mathematical Finance Series: Lecture Notes in Mathematics 1919

      Pages: 103-172

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians.2007

    • Author(s)
      H. Ishii, et. al.
    • Journal Title

      Indiana Univ. Math. J. 56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A remark on Impulse control problems with risk-sensitive criteria2007

    • Author(s)
      H., Nagai
    • Journal Title

      Eds. J. Akahori, S. Ogawa and S. Watanabe, "Stochastic Processes and Applications to Mathematical Finance" World Scientific

      Pages: 219-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Stopping problems of certain multiplicative functionals and optimal investment with transaction costs2007

    • Author(s)
      H., Nagai
    • Journal Title

      Applied Mathematics and Optimization 55

      Pages: 359-384

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A linear-quadratic control problem with discretionary stopping2007

    • Author(s)
      S., Koike, et. al.
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series B 8-2

      Pages: 261-277

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Maximum principle for fully nonlinear equations via the iterated comparison function method2007

    • Author(s)
      S., Koike, et. al.
    • Journal Title

      Mathematische Annalen 339

      Pages: 461-484

    • NAID

      120006385615

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula2007

    • Author(s)
      H., Matsumoto
    • Journal Title

      J. Func. Anal 244

      Pages: 565-578

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Models for insider trading with finite utility2007

    • Author(s)
      A., Kohatsu-Higa
    • Journal Title

      Paris-Princeton Lectures on Mathem atical Finance Series : Lecture Notes in Mathematics Vol.1919

      Pages: 103-172

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians2007

    • Author(s)
      Ishii, Hitoshi, et. al.
    • Journal Title

      Indiana Univ. Math. J No.56

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Kreins strings with singular left boundary2007

    • Author(s)
      S., Kotani
    • Journal Title

      Report on Math. Phys No.59

      Pages: 305-316

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A remark on Impulse cpntrol problems with risk-sensitive criteria2007

    • Author(s)
      Hideo NAGAI
    • Journal Title

      "Stochastic Processes and Applications to Mathematical Finance", Eds. J. Akahori,., World Scientific

      Pages: 219-232

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximum principle for fully nonlinear equations via the iterated comparison function method2007

    • Author(s)
      S. Koike,.
    • Journal Title

      Mathematische Annalen 339

      Pages: 461-484

    • NAID

      120006385615

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A linear-quadratic control problem with discretionary stopping,2007

    • Author(s)
      S. Koike,.
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series B 8

      Pages: 261-277

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula,2007

    • Author(s)
      H. Matsumoto
    • Journal Title

      Journal of Functional Analysis 244

      Pages: 565-578

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Krein's strings with singular left boundary2007

    • Author(s)
      S. Kotani
    • Journal Title

      Report on Math. Phys. 59

      Pages: 305-316

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Models for insider trading with finite utility2007

    • Author(s)
      Kohatsu-Higa Arturo
    • Journal Title

      Paris-Princeton Lectures on Mathematical Finance Series: Lecture Notes in Mathematics 1919

      Pages: 103-172

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimating Multi-dimensional density functions for random variables in Wiener space2007

    • Author(s)
      Kohatsu-Higa Arturo,.
    • Journal Title

      C.R. Acad. Sci., Paris (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians2007

    • Author(s)
      H. Ishii,.
    • Journal Title

      Indiana Univ Math. J. 56

      Pages: 2159-2183

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The probability of two F_q-polynomials to be coprime,2007

    • Author(s)
      H. Sugita.
    • Journal Title

      Proceedings of the International Conference on Probability and Number Theory, ASPM 49

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stopping problems of certain multiplicative functionals and optimal investment with transaction costs2007

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Applied Mathematics and Optimization (in press)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] PDE approach to utility maximization for market models with hidden Markov factors2007

    • Author(s)
      H.Nagai, et al.
    • Journal Title

      "Progress in Probability", Birkhauser (In press)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A remark on impulse control problems with risk-sensitive criteria2007

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Proceedings of Ritsumeikan Conference on Stochastic proce sses and applications to mathematical finance (in press)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula2007

    • Author(s)
      H.Matsumoto
    • Journal Title

      Journal of Functional Analysis 244

      Pages: 565-578

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Risk-sensitive quasi-variational inequalities for optimal investment with general transaction costs2006

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Asymptotic Analysis 48

      Pages: 243-265

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2006 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Utility maximization in an insider influenced market2006

    • Author(s)
      A. Kohatsu-Higa, et. al.
    • Journal Title

      Mathematical Finance 16

      Pages: 163-179

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A duality approach for the weak approximations of stochastic differential equations2006

    • Author(s)
      E. Clement, et. al.
    • Journal Title

      Annals of Applied Probability 16

      Pages: 1124-1154

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On a condition that one-dimensional diffusion processes are martingales2006

    • Author(s)
      S. Kotani
    • Journal Title

      Seminaire de Probabilites XXXIX, LNM 1874

      Pages: 149-156

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space2006

    • Author(s)
      Fujita, Yasuhiro
    • Journal Title

      Indiana Univ. Math. J. 55

      Pages: 1671-1700

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator2006

    • Author(s)
      Fujita, Yasuhiro, et. al.
    • Journal Title

      Comm. Partial Differential Equations 31

      Pages: 827-848

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Risk-sensitive quasi-variational inequalities for optimal investment with general transaction costs2006

    • Author(s)
      H., Nagai
    • Journal Title

      Asymptotic Analysis vol.48

      Pages: 243-265

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A duality approach for the weak approximations of stochastic differential equations2006

    • Author(s)
      E., Clement, et. al.
    • Journal Title

      Annals of Applied Probability Vol.16, No.3

      Pages: 1124-1154

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Utility maximization in an insider influenced market2006

    • Author(s)
      A., Kohatsu-Higa, et. al.
    • Journal Title

      Mathematical Finance Vol.16

      Pages: 163-179

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $n$ space2006

    • Author(s)
      Fujita, Yasuhiro, et. al.
    • Journal Title

      Indiana Univ. Math. J No.55

      Pages: 1671-1700

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator2006

    • Author(s)
      Fujita, Yasuhiro, et. al.
    • Journal Title

      Comm. Partial Differential Equations No.31

      Pages: 827-848

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On a condition that one-dimensional diffusion processes are martingales2006

    • Author(s)
      S., Kotani
    • Journal Title

      Seminaire de Probabilites XXXIX, LNM No.1874

      Pages: 149-156

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] PDE approach to utility maximization with partial information2006

    • Author(s)
      H.Nagai, et al.
    • Journal Title

      数理解析研究所講究録 1462

      Pages: 116-130

    • Related Report
      2006 Annual Research Report 2005 Annual Research Report
  • [Journal Article] Utility maximization in an insider influenced market2006

    • Author(s)
      A.Kohatsu-Higa, et al.
    • Journal Title

      Mathematical Finance 16

      Pages: 163-179

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A duality approach for the weak approximations of stochastic differential equations2006

    • Author(s)
      E.Clement, et al.
    • Journal Title

      Annals of Applied Probability 16・3

      Pages: 1124-1154

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The probabilistic solution of the Dirichlet problem for degenerat e elliptic equations2006

    • Author(s)
      Liu, Chuandi, et al.
    • Journal Title

      Bull. Pol. Acad. Sci. Math. 54

      Pages: 163-174

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On a condition that one-dimensional diffusion processes are martingales, 1874(2006), 149-1562006

    • Author(s)
      S.Kotani
    • Journal Title

      Seminaire de Probabilites XXXIX,・LNM 1874

      Pages: 149-156

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Asymptotic solutions of Hamilton-Jacobi equations in Euclidean nspace2006

    • Author(s)
      Y.Fujita, et al.
    • Journal Title

      Indiana Univ. Math. Journal 55

      Pages: 1671-1700

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator2006

    • Author(s)
      Y.Fujita, et al.
    • Journal Title

      Comm. Partial differential equations 31

      Pages: 827-848

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A duality approach for the weak approximations of stochastic differential equations2006

    • Author(s)
      E.Clement, et al.
    • Journal Title

      Annals of Applied Probability (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Utility Maximization in an insider influenced market2006

    • Author(s)
      A.Kohatsu-Higa, et al.
    • Journal Title

      Mathematical Finance (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On some laws of iterated logarithmfor Burgers turbulence with Brownian initial data based on the concave majorant2006

    • Author(s)
      Y.Isozaki
    • Journal Title

      Osaka Journal of Mathematics 43(In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Limit of solutions of $p$ Laplace equations as $p$ goes to infinity and related variational problems2005

    • Author(s)
      H. Ishii, et. al.
    • Journal Title

      SIAM Journal of mathematical Analysis 37

      Pages: 411-437

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Optimal consumption and portfolio choice with stopping2005

    • Author(s)
      S. Koike, et. al.
    • Journal Title

      Funkcialaj Ekvacioj 48

      Pages: 183-202

    • NAID

      130000141285

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Exponential functionals of Brownian motion, I: Probability laws at fixed time, II: Some related diffusion processes2005

    • Author(s)
      H. Matsumoto, et. al.
    • Journal Title

      Probability Surveys 2

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Optimal consumption and portfolio choice with stopping2005

    • Author(s)
      S., Koike, et. al.
    • Journal Title

      Funkcialaj Ekvacioj 48

      Pages: 183-202

    • NAID

      130000141285

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motion I : Probability laws at fixed time.2005

    • Author(s)
      H., Matsumoto, et. al.
    • Journal Title

      Probability Surveys 2

      Pages: 312-347

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Exponential functionals of Brownian motionII : Some related diffusion processes2005

    • Author(s)
      H., Matsumoto, et. al.
    • Journal Title

      Probability Surveys 2

      Pages: 348-384

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Limits of solutions of $p$-Laplace equations as $p$ goes to infinity and related variational problems2005

    • Author(s)
      Ishii., Hitoshi, et. al.
    • Journal Title

      SIAM J. Math. Anal No.37

      Pages: 411-437

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Limit of solutions of $p$ Laplace equations as $p$ goes to infinity and related variational problems2005

    • Author(s)
      H.Ishii, et al.
    • Journal Title

      SIAM Journal of mathematical Analysis 37

      Pages: 411-437

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Optimal consumption and choice with stopping2005

    • Author(s)
      S.Koike, et al.
    • Journal Title

      Funkcialaj Ekvacioj 48

      Pages: 183-202

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Projection scheme for a reflected stochastic heat equation with additive noise2005

    • Author(s)
      Kohatsu-Higa, A, et al.
    • Journal Title

      Foundation of probability and physics 3

      Pages: 158-167

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Densities of one dimensional backward SDEs2005

    • Author(s)
      Antonelli, F., et al.
    • Journal Title

      Potential Analysis 22

      Pages: 263-87

    • Related Report
      2005 Annual Research Report
  • [Journal Article] An extension of linear regulator for degenerate diffusion2005

    • Author(s)
      Baten, MD.A., et al.
    • Journal Title

      IEEE Transaction on Automatic Control 50

      Pages: 1822-1826

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Risk-sensitive portfolio optimization with full and partial information, "Stochastic Analysis and Related Topics"2004

    • Author(s)
      H. Nagai
    • Journal Title

      Advanced Studies in Pure Mathematics 41

      Pages: 257-278

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Risky fraction processes and Problems with Transaction Costs2004

    • Author(s)
      H. Nagai
    • Journal Title

      "Stochastic Processes and Applications to Mathematical Finance", Eds. J. Akahori, S. Ogawa and S. Watanabe, World Scientific

      Pages: 271-288

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Maximum principle and existence of $L^p$-viscosity solutions for fully nonlinear, uniformly elliptic equations with measurable and quadratic terms2004

    • Author(s)
      S. Koike, et. al.
    • Journal Title

      Nonlinear Differential Equations and Applications 11

      Pages: 491-509

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Markov or non-Markov property of $cM-X$ processes2004

    • Author(s)
      H. Matsumoto
    • Journal Title

      J. Math. Soc. Japan 56

      Pages: 519-540

    • NAID

      10013123100

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Risk-sensitive portfolio optimization with full and partial information, "Stochastic Analysis and Related Topics2004

    • Author(s)
      H., Nagai
    • Journal Title

      Advanced Studies in Pure Mathematics 41

      Pages: 257-278

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Risky fraction processes and Problems with Transaction Costs2004

    • Author(s)
      H., Nagai
    • Journal Title

      "Stochastic Processes and Applications to

      Pages: 271-288

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Maximum principle and existence of 51./14-viscosity solutions for fully nonlinear, uniformly elliptic equations with measurable and quadratic terms2004

    • Author(s)
      S., Koike, et. al.
    • Journal Title

      Nonlinear Differential Equations and Applications 11-4

      Pages: 491-509

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Markov or non-Markov property of $cM-X$ procesesses2004

    • Author(s)
      H., Matsumoto
    • Journal Title

      J. Math. Soc. Japan No.56

      Pages: 519-540

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Risk-sensitive portfolio optimization with full and partial information2004

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Advanced Studies in Pure Mathematics 41

      Pages: 257-278

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Risky fraction processes and Problems with Transaction Costs2004

    • Author(s)
      Hideo NAGAI
    • Journal Title

      Stochastic Processes and Applications to Mathematical Finance

      Pages: 271-288

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Dynamic minimization of worst conditional expectation of shortfall2004

    • Author(s)
      Jun SEKINE
    • Journal Title

      Mathematical Finance 14/4

      Pages: 605-618

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Maximum principle and existence of $L^p$-viscosity solutions for fully nonlinear, uniformly elliptic equations with measurable and quadratic terms2004

    • Author(s)
      S.Koike, A.Swiech
    • Journal Title

      Nonlinear Differential Equations and Applications 11/4

      Pages: 491-509

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Markov or non-Markov property of $cM-X$ processes2004

    • Author(s)
      H.Matsumoto, Y.Ogura
    • Journal Title

      J.Mathematical Society of Japan 56

      Pages: 519-540

    • NAID

      10013123100

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain2004

    • Author(s)
      H.Ishii, M.-H.Sato
    • Journal Title

      Nonlinear Analysis 57

      Pages: 1077-1098

    • Related Report
      2004 Annual Research Report
  • [Journal Article] An Optimal Control Variance Reduction Method for Density Estimation

    • Author(s)
      A., Kebaier, et. al.
    • Journal Title

      Stochastic Processes and their applications, (2008) (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Enlargement of filtrations with random times for processes with jumps

    • Author(s)
      A., Kohatsu-Higa, et. al.
    • Journal Title

      Stochastic Processes and their applications. (2008) (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A large trader-insider model

    • Author(s)
      A.Kohatsu-Higa, et al.
    • Journal Title

      Proceedings of the Ritsumeikan Conference on Stochastic Process and mathematical Finance 2005 (In press)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Risk-sensitive quasi-variational inequalities for optimal investment with general transaction costs

    • Author(s)
      H.Nagai
    • Journal Title

      Asymptotic Analysis (In press)

    • Related Report
      2005 Annual Research Report
  • [Presentation] Minimizing a down-side risk probability and risk-sensitive asset allocation under partial information2008

    • Author(s)
      Hideo NAGAI
    • Organizer
      Ajou-KAIST-POSTECH International Conference in Finance and Mathematics,
    • Place of Presentation
      Ajou University, Korea
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Minimizing a down-side risk probability and risk-sensitive asset allocation under partial information2008

    • Author(s)
      Hideo, NAGAI
    • Organizer
      Ajou-KAIST-POSTECH International Conference in Finance and Mathematics
    • Place of Presentation
      Ajou University and POSTECH, Korea
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations and related topics2007

    • Author(s)
      H. Ishii
    • Organizer
      First Chile-Japan workshop on nonlinear elliptic and parabolic PDE
    • Place of Presentation
      サンチアーゴ,チリ
    • Year and Date
      2007-10-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations and related topics2007

    • Author(s)
      Hitoshi, Ishii
    • Organizer
      First Chile-Japan workshop on nonlinear elliptic and parabolic PDE
    • Place of Presentation
      Santiago, Chile
    • Year and Date
      2007-10-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Randomization of number theoretic special functions2007

    • Author(s)
      H. Sugita
    • Organizer
      数論と確率論
    • Place of Presentation
      国際高等研
    • Year and Date
      2007-10-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics2007

    • Author(s)
      H. Ishii
    • Organizer
      6th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      チューリッヒ,スイス,
    • Year and Date
      2007-07-19
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics2007

    • Author(s)
      Hitoshi, Ishii
    • Organizer
      6th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Zurich, Switzerland
    • Year and Date
      2007-07-19
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics2007

    • Author(s)
      H. Ishii
    • Organizer
      6th InternationalCongress on Industrial and Applied Mathematics
    • Place of Presentation
      チューリッヒ,スイス,
    • Year and Date
      2007-07-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotics of the probability minimizing a down-side risk: Partial information case2007

    • Author(s)
      Hideo NAGAI
    • Organizer
      Conference "Stochastic Processes: theory and applications"
    • Place of Presentation
      Bressanone, Italy
    • Year and Date
      2007-07-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Survey on 1-dim. Random Schrodinger Operators and Lyapunov Exponents2007

    • Author(s)
      S. Kotani
    • Organizer
      International Conference on the Occasion of the 150th Birthday of A.M. Lyapunov
    • Place of Presentation
      ハルコフ、ウクライナ
    • Year and Date
      2007-06-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Survey on 1-dim. Random Schrodinger Operators and Lyapunov Exponents2007

    • Author(s)
      S. Kotani
    • Organizer
      International Conference on the Occasion of the 150th Birthday of A. M. Lyapunov
    • Place of Presentation
      ハルコフ、ウクライナ
    • Year and Date
      2007-06-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Minimizing down-side risk probability and risk-sensitive asset allocation for linear Gaussian models2007

    • Author(s)
      Hideo NAGAI
    • Organizer
      Advances in Mathematics of Finance, Second General AMAMEF Conference and Banach Center Conference
    • Place of Presentation
      Bedlewo, Poland
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Asymptotics of the probability minimizing a down-side risk: Partial information case2007

    • Author(s)
      Hideo NAGAI
    • Organizer
      Conference "Stochastic Processes: theory and applications"
    • Place of Presentation
      Bressanone, Italy,
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Minimizing a down-side risk probability and H-J-B equations of risk-sensitive asset allocation2007

    • Author(s)
      Hideo NAGAI
    • Organizer
      「非線形偏微分方程式とその応用」
    • Place of Presentation
      神戸大学海事科学研究科
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Maximum principle for $L^p$-viscosity solutions of fully nonlinear equations with unbounded coefficients2007

    • Author(s)
      Shigeaki Koike
    • Organizer
      International Conference of Reaction Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University, 台湾
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotics of the probability minimizing a down-side risk : Partial information case2007

    • Author(s)
      Hideo, NAGAI
    • Organizer
      Conference "Stochastic Processes : theory and applications"
    • Place of Presentation
      Bressanone, Italy
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Minimizing a down-side risk probability and H-J-B equations of risk-sensitive asset allocation2007

    • Author(s)
      Hideo, NAGAI
    • Organizer
      1Nonlinear partial differential equations and applications)
    • Place of Presentation
      Kobe University, Japan
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Survey on 1-dim : Random Sahr&dinger Operators and Lyapunov Exponents2007

    • Author(s)
      Shinichi, Kotani
    • Organizer
      International Conference on the Occasion of the 150th Birthday ofA.M.Lyapunov
    • Place of Presentation
      Ukraine
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Maximum principle for L^p-viscosity solutions of fully nonlinear equations with unbounded coefficients2007

    • Author(s)
      S., Koike
    • Organizer
      International Conference of Reaction Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University, Taiwan
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations2006

    • Author(s)
      Hitoshi Ishii
    • Organizer
      International Congress of Mathematicians 2006
    • Place of Presentation
      マドリッド,スペイン
    • Year and Date
      2006-08-22
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Recent results on asymmetric information and insider trading. Plenary speaker.2006

    • Author(s)
      Arturo Kohatsu-Higa
    • Organizer
      Bachelier Congress
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2006-08-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Recent results on asymmetric information and insider trading. Plenary speaker2006

    • Author(s)
      Arturo, Kohatsu-Higa
    • Organizer
      Bachelier Congress
    • Place of Presentation
      Tokyo Japan
    • Year and Date
      2006-08-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Krein's spectral theory and its generalization2006

    • Author(s)
      S. Kotani
    • Organizer
      21st Max Born Symposium
    • Place of Presentation
      ブロツラフ、ポーランド
    • Year and Date
      2006-06-26
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean $n$ space2006

    • Author(s)
      Hitoshi Ishii
    • Organizer
      Partial differential equations and applications
    • Place of Presentation
      Universita di Roma, La Sapienza,ローマ,イタリア
    • Year and Date
      2006-03-11
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Optimal investment with general transaction costs and risk-sensitive quasi-variational inequalities2006

    • Author(s)
      Hideo NAGAI
    • Organizer
      Workshop on mathematical Finance and Insurance
    • Place of Presentation
      Lijiang, Yunnan, China
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Risk-sensitive quasi-variational inequalities for optimal investment with general transaction costs2006

    • Author(s)
      Hideo NAGAI
    • Organizer
      International Symposium on Stochastic Processes and Applications to Mathematical Finance
    • Place of Presentation
      立命館大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Risk-sensitive quasi-variational inequalities for optimal investment with general transaction costs2006

    • Author(s)
      Hideo, NAGAI
    • Organizer
      International Symposium on Stochastic Processes and Applications to Mathematical Finance, Ritsumeikan University
    • Place of Presentation
      Kusatsu, Japan
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations2006

    • Author(s)
      Hitoshi, Ishii
    • Organizer
      International Congress of Mathematicians
    • Place of Presentation
      Madrid, Spain
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean $n$ space2006

    • Author(s)
      Hitoshi, Ishii
    • Organizer
      Partial differential equations and
    • Place of Presentation
      La Sapienza, Rome, Italy
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Krein's spectral theory and its generalization2006

    • Author(s)
      Shinichi, Kotani
    • Organizer
      21st Max Born Symposium
    • Place of Presentation
      Wroclaw, Poland
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Risk-sensitive variational inequalities arising from optimal investment with transaction costs2005

    • Author(s)
      Hideo NAGAI
    • Organizer
      Fourth Colloquium on Backward Stochastic Differential Equations and Applications
    • Place of Presentation
      Shanghai, China
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] PDE approach to utility maximization for market models with hidden Markov factors2005

    • Author(s)
      Hideo NAGAI
    • Organizer
      2005 Daiwa International Workshop on Financial Engineering
    • Place of Presentation
      Otemachi, Sankei Plaza, Tokyo, Japan.
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Stopping problems and optimal investment with transaction costs2005

    • Author(s)
      Hideo NAGAI
    • Organizer
      Stochastic Processes and Applications to Mathematical Finance
    • Place of Presentation
      Ritsumeikan Univ. Kusatsu, Japan
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] PDE approach to utility maximization for market models with hidden Markov factors2005

    • Author(s)
      Hideo, NAGAI
    • Organizer
      2005 Daiwa International Workshop on Financial Engineering
    • Place of Presentation
      Otemachi, Sankei Plaza, Tokyo,Japan
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Risky Fraction Processes and Portfolio Optimization with Transaction Costs2004

    • Author(s)
      Hideo NAGAI
    • Organizer
      2004 Daiwa International Workshop on Financial Engineering
    • Place of Presentation
      Tokyo, Sankei Plaza, Japan
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 微分方程式と固有関数展開2006

    • Author(s)
      小谷 真一
    • Total Pages
      232
    • Publisher
      岩波書店
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] Differential equations and eigenfunctionexpansion2006

    • Author(s)
      S., Kotani
    • Publisher
      Iwanami
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] A Beginner's Guide to the Theory of Viscosity Solutions2004

    • Author(s)
      S.Koike
    • Total Pages
      123
    • Publisher
      日本数学会
    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2021-04-07  

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