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Equilibrium Multi-Agent Model with Heterogeneous Views on Fundamental Risks

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 investigates an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating uncertainties on fundamental risks, where multiple agents have heterogeneous (conservative, neutral, aggressive) views on the risks represented by Brownian motions. Each agent maximizes its expected utility on consumption under its subjective probability measure. Specifically, we formulate the individual optimization problem as a sup-sup-inf problem, which is an optimal consumption and portfolio problem with a choice of a probability measure. Moreover, we provide an expression of the state-price density process in a market equilibrium, which derives the representations of the interest rate and the market price of risk. To the best of our knowledge, this is the first attempt to investigate the multi-agent model with heterogeneous views on the risks by considering a market equilibrium and solving sup-sup-inf problems on the choice of a probability measure. We emphasize that the setting, where each agent has heterogeneous views on different risks, incorporates a special case where each agent has only conservative or neutral views on risks with different degrees of conservativeness. Also, the setting includes the case where the agents have aggressive views on risks, commonly observed as bullish sentiments in the financial markets in the monetary easing after the global financial crisis and particularly in the COVID-19 pandemic. Finally, we present numerical examples of the interest rate model, which show how heterogeneous views of the multiple agents on the risks affect the shape of the yield curve.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2021cf1173
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    References listed on IDEAS

    as
    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. 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. 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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