Multi-agent Equilibrium Model with Heterogeneous Views on Fundamental Risks in Incomplete Market

Keisuke Kizaki, Taiga Saito and Akihiko Takahashi
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Keisuke Kizaki: Mizuho-DL Financial Technology
Taiga Saito: School of Commerce, Senshu University
Akihiko Takahashi: Faculty of Economics, The University of Tokyo

No CIRJE-F-1224, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper considers a multi-agent optimal investment problem with conserva- tive, 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 in mum 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 rst 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 senti- ments 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 trad- ing 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.

Pages: 50 pages
Date: 2024-03
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