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Multi-agent Equilibrium Model with Heterogeneous Views on Fundamental Risks 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, aggressive, or neutral sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative, aggressive, or neutral sentiments of the agents by a sup-inf/inf-sup, sup-sup, or sup problem where we take infimum or supremum on a choice of a probability measure depending on the view types 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 where a group of agents has either conservative, aggressive, or neutral sentiments on the fundamental risks and a general case where the Sharpe ratio process of the risky asset and the optimal trading strategies in equilibrium are explicitly solved by a BSDE approach. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under heterogeneous sentiments, which explain how the conservative, aggressive, or neutral sentiments affect the Sharpe ratio process of the risky asset and the trading strategies of the agents in equilibrium.

Suggested Citation

  • Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2024. "Multi-agent Equilibrium Model with Heterogeneous Views on Fundamental Risks in Incomplete Market," CARF F-Series CARF-F-578, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf578
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    References listed on IDEAS

    as
    1. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
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    3. 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.
    4. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    5. 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.
    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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