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Portfolio Optimization with Choice of a Probability Measure

Author

Listed:
  • Taiga Saito

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

This paper considers a new problem for portfolio optimization with a choice of a probability measure, partic- ularly optimal investment problem under sentiments. Firstly, we formulate the problem as a sup-sup-inf problem consisting of optimal investment and a choice of a probability measure expressing aggressive and conservative attitudes of the investor. This problem also includes the case where the agent has conservative and neutral views on risks represented by Brownian motions and degrees of conservativeness differ among the risk. Secondly, we obtain an expression of the volatility process of a backward stochastic differential equation related to the conservative sentiment in order to investigate cases where the sup-sup-inf problem is solved. Specifically, we take a Malliavin calculus approach to solve the problem and obtain an optimal portfolio process. Finally, we provide an expression of the optimal portfolio under the sentiments in two examples with stochastic uncertainties in an exponential utility case and investigate the impact of the sentiments on the portfolio process.

Suggested Citation

  • Taiga Saito & Akihiko Takahashi, 2021. "Portfolio Optimization with Choice of a Probability Measure," CIRJE F-Series CIRJE-F-1165, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2021cf1165
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2021/2021cf1165.pdf
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    References listed on IDEAS

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    1. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2020. "Interest Rate Model with Investor Attitude and Text Mining," CIRJE F-Series CIRJE-F-1152, CIRJE, Faculty of Economics, University of Tokyo.
    2. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    3. Kiyohiko G. Nishimura & Seisho Sato & Akihiko Takahashi, 2019. "Term Structure Models During the Global Financial Crisis: A Parsimonious Text Mining Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 297-337, September.
    4. Taiga Saito & Akihiko Takahashi, 2017. "Derivatives Pricing with Market Impact and Limit Order Book," CARF F-Series CARF-F-385, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Alos, Elisa & Ewald, Christian-Oliver, 2007. "Malliavin differentiability of the Heston volatility and applications to option pricing," MPRA Paper 3237, University Library of Munich, Germany.
    6. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2020. "Interest Rate Model with Investor Attitude and Text Mining (Published in IEEE Access)," CARF F-Series CARF-F-479, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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    Cited by:

    1. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2022. "Multi-agent Robust Optimal Investment Problem in Incomplete Market," CIRJE F-Series CIRJE-F-1198, CIRJE, Faculty of Economics, University of Tokyo.
    2. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2021. "Equilibrium Multi-Agent Model with Heterogeneous Views on Fundamental Risks," CIRJE F-Series CIRJE-F-1173, CIRJE, Faculty of Economics, University of Tokyo.
    3. Taiga Saito & Akihiko Takahashi, 2022. "Portfolio optimization with choice of a probability measure (forthcoming in proceedings of IEEE CIFEr 2022)," CARF F-Series CARF-F-534, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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