Arai, Takuji

写真a

Affiliation

Faculty of Economics (Mita)

Position

Professor

Related Websites

 

Research Areas 【 Display / hide

  • Mathematical analysis (Mathematical Finance)

Research Keywords 【 Display / hide

  • Mathematical Finance

  • Probability Theory

 

Papers 【 Display / hide

  • Optimal initial capital induced by the optimized certainty equivalent

    Arai T., Asano T., Nishide K.

    Insurance: Mathematics and Economics (Insurance: Mathematics and Economics)  85   115 - 125 2019.03

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  01676687

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    © 2019 Elsevier B.V. This paper proposes the notion of optimal initial capital (OIC) induced by the optimized certainty equivalent (OCE), as discussed in Ben-Tal and Teboulle (1986) and Ben-Tal and Teboulle (2007). It also investigates the properties of the OIC with various types of utility functions. It is shown that the OIC can be a monetary utility function (negative value of risk measure) for future payoffs with the decision maker's concrete criteria in the background.

  • A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus

    Arai T., Imai Y.

    Applied Mathematical Finance (Applied Mathematical Finance)  25 ( 3 ) 247 - 267 2018.05

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  1350486X

     View Summary

    © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

  • Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models

    Takuji Arai, Yuto Imai and Ryo Nakashima

    Advances in Mathematical Economics 22   1 - 24 2018

    Research paper (scientific journal), Joint Work, Accepted

  • On the difference between locally risk-minimizing and delta hedging strategies for exponential Levy models

    Takuji Arai and Yuto Imai

    Japan Journal of Industrial and Applied Mathematics 34 ( 3 ) 845 - 858 2017

    Research paper (scientific journal), Joint Work, Accepted

  • Local risk-minimization for Barndorff-Nielsen and Shephard models

    Takuji Arai, Yuto Imai and Ryoichi Suzuki

    , Finance & Stochastics 21   551 - 592 2017

    Research paper (scientific journal), Joint Work, Accepted

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Papers, etc., Registered in KOARA 【 Display / hide

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • 確率ボラティリティモデルに対する最適ヘッジ戦略の導出と数値計算法の研究

    2018.04
    -
    2021.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 新井 拓児, Grant-in-Aid for Scientific Research (C), Principal Investigator

  • Malliavin解析による最適ヘッジ戦略の導出とその数値計算法の研究

    2015.04
    -
    2019.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 新井 拓児, Grant-in-Aid for Scientific Research (C), Principal Investigator

 

Courses Taught 【 Display / hide

  • SEMINAR: ECONOMETRICS

    2021

  • RESEARCH SEMINAR D

    2021

  • RESEARCH SEMINAR C

    2021

  • RESEARCH SEMINAR (THESIS)

    2021

  • MATHEMATICS FOR ECONOMICS

    2021

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