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A Study of Levy Processes in Finance

Research Project

Project/Area Number 26380402
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Money/ Finance
Research InstitutionHosei University

Principal Investigator

YAMAZAKI Akira  法政大学, 経営学部, 教授 (60633592)

Research Collaborator YOSHIKAWA Daisuke  北海学園大学, 経営学部, 准教授
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsファイナンス / 確率解析 / レヴィ過程 / 時間変更レヴィ過程 / デリバティブ / 資産価格 / 最適配当政策 / プライシング・カーネル / 最適配当 / オプション / リスク回避度 / 資産価格理論
Outline of Final Research Achievements

This study has addressed an application of Levy and time-changed Levy processes to the field of finance and extended classical financial theory based on normal distributions. Levy processes are a class of non-Gaussian stochastic processes for describing jumps in asset price dynamics and dividend streams, and time-changed Levy processes are their generalization with stochastic time change, which can be regarded as a generalization of stochastic volatility. They have been applied to the four problems: path-dependent option pricing, asset pricing in exchange economy, optimal dividend policy for a firm, and reproducing U-shaped pricing kernels. In these problems, analytical representations of derivative prices, asset prices, and decision rules for optimal policy were derived from financial models we proposed. In addition, numerical examples were provided for deeply understanding our mathematical results. As a result, four academic papers were published in international journals.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report

Research Products

(8 results)

All 2017 2016 2015 2014 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 4 results) Presentation (1 results) (of which Invited: 1 results) Remarks (3 results)

  • [Journal Article] Equilibrium Equity Price with Optimal Dividend Policy2017

    • Author(s)
      Akira Yamazaki
    • Journal Title

      International Journal of Theoretical and Applied Finance

      Volume: 20

    • DOI

      10.1142/s0219024917500121

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Generalized Barndorff-Nielsen and Shephard Model and Discretely Monitored Option Pricing2016

    • Author(s)
      Akira Yamazaki
    • Journal Title

      International Journal of Theoretical and Applied Finance

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Asset Pricing with Non-Geometric Type of Dividends2015

    • Author(s)
      Akira Yamazaki
    • Journal Title

      Annals of Financial Economics

      Volume: 10

    • DOI

      10.1142/s2010495215500165

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Levy Processes2015

    • Author(s)
      Yuji Umezawa and Akira Yamazaki
    • Journal Title

      Applied Mathematical Finance

      Volume: 22 Pages: 133-161

    • DOI

      10.1080/1350486x.2014.960529

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Lucas Trees with Exponential Utility2014

    • Author(s)
      山嵜 輝
    • Organizer
      中之島ワークショップ:金融工学・数理計量ファイナンスの諸問題2014
    • Place of Presentation
      大阪大学(大阪府大阪市北区)
    • Year and Date
      2014-12-04 – 2014-12-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks] 山嵜輝研究室ホームページ

    • URL

      http://akira2yamazaki.com/index.html

    • Related Report
      2016 Annual Research Report
  • [Remarks] 法政大学 経営学部 山嵜 輝 研究室ホームページ

    • URL

      http://akira2yamazaki.com/

    • Related Report
      2015 Research-status Report
  • [Remarks] 法政大学 経営学部 山嵜 輝 研究室

    • URL

      http://akira2yamazaki.com/

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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