| Project/Area Number |
11640132
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya City University |
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Principal Investigator |
MISAWA Tetsuya Nagoya City Univ., Fact., of Economics, Prof., 経済学部, 教授 (10190620)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshiaki Nagoya City Univ., Inst. of Natural Sci., Prof., 自然科学研究教育センター, 教授 (50106259)
SHIMIZU Akinobu Nagoya City Univ., Inst. of Natural Sci., Prof.., 自然科学研究教育センター, 教授 (10015547)
MIYAHARA Yoshio Nagoya City Univ., Fact., of Economics, Prof., 経済学部, 教授 (20106256)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | Nonlinear stochastic systems / Composition methods / Stochastic numerics / Geometric Levy processes / Mathematical finance / Fleming-Biot processes / Recurrent Markov chain / Bochner-Schwartz' teorem / オプション価格付け / Flemming-Viot過程 / Grusin作用素 / Nonlinear stochastic system / Composition methods / Computational finance / Geometric Levy process / Incomplete market / Positively recurrent Markov chain / Stochastic logistic process / Nonlinear partial differential equations / Composition method / Stochastic exponential map / Mathematical finance / 熱核法 / 正定値超関数 |
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| Research Abstract |
The present study focuses on a theory of conserved quantities and symmetries for stochastic non-linear dynamical systems, which are described by stochastic differential equations, and the related topics. Particularly, the head investigator, Misawa, deeply investigates "composition methods" in order to produce numerical approximation schemes for such stochastic non-linear dynamical systems. In the proposed methods, the solution is approximated by composition of the stochastic flows derived from simpler and exactly integrable vector field operators which are related to the concepts of conserved quantities and symmetries. The new obtainable schemes are advantageous to preserve the special character/structure of the stochastic systems numerically and are useful for approximations of the solutions. To examine the superiority, Misawa carries out several numerical simulations on the basis of the proposed schemes for stochastic systems which arise in the mathematical finance.
As the related top
… More
ics, Misawa also treats the stochastic numerical simulations of stochastic macroeconomic models with noise effects and smoothing analysis of time Series data by wavelet systems. The investigator, Miyahara, studies on the option pricing theory of incomplete markets. The price processes of the underlying assets are assumed to be geometric Levy processes, and the price of options are supposed to be determined as by the minimal relative entropy principle. He has named this pricing model the [Geometric Levy Process ＆ MEMM] Pricing Model, and investigated the properties of this model. The investigator, Shimizu, works with some genealogical problems related to measure-valued diffusion processes and examines the fractional moments of the first returning time of positively recurrent Markov chains. The investigator, Hashimoto, shows Gevrey hypoellipticity for Grushin Operators by FBI transformation.
Through these related topics, we find out that stochastic dynamical theory and stochastic numerics are useful for the analysis of the several stochastic models. Less
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