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Multi-agent Robust Optimal Investment Problem in Incomplete Market

Author

Listed:
  • Keisuke Kizaki

    (Mizuho-DL Financial Technology)

  • Taiga Saito

    (School of Commerce, Senshu University)

  • Akihiko Takahashi

    (Graduate School of Economics, The University of Tokyo)

Abstract

This paper considers a multi-agent optimal investment problem with conservative 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 investigate 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, 2023. "Multi-agent Robust Optimal Investment Problem in Incomplete Market," CARF F-Series CARF-F-575, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf575
    as

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    References listed on IDEAS

    as
    1. 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..
    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. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    4. 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.
    5. 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.
    6. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    Full references (including those not matched with items on IDEAS)

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