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Multi-agent Robust Optimal Investment Problem in Incomplete Market

Author

Listed:
  • Keisuke Kizaki

    (Graduate School of Economics, The University of Tokyo)

  • Taiga Saito

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

This paper considers a multi-agent optimal investment problem with conserva- tive sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative sentiments of the agents by a sup-inf/inf-sup problem where we take infimum on a choice of a probability measure and supremum on trading strategies. To the best of our knowledge, this is the first attempt to inves- tigate a multi-agent equilibrium model in an incomplete setting with heterogeneous views on Brownian motions. Moreover, we show a square-root case and a general case where the trading strategies and the excess return process of the risky asset in equilibrium are explicitly solved. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under conservative sentiments, which explain how the sentiments affect the trading strategies of the agents and the expected return process of the risky asset.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2022cf1198
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2022/2022cf1198.pdf
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    References listed on IDEAS

    as
    1. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    2. 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.
    3. 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.
    4. 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.
    5. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    6. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    7. 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. "A Multi-agent Incomplete Equilibrium Model and Its Applications to Reinsurance Pricing and Life-Cycle Investment," CIRJE F-Series CIRJE-F-1206, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kizaki, Keisuke & Saito, Taiga & Takahashi, Akihiko, 2024. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 132-155.
    3. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2022. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment," CARF F-Series CARF-F-551, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2023.

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