Discussion Papers 2022

CIRJE-F-1198	"Multi-agent Robust Optimal Investment Problem in Incomplete Market"
Author Name	Kizaki, Keisuke, Taiga Saito, Akihiko Takahashi
Date	September 2022
Full Paper	PDF file
Remarks	Revised in November 2022 and November 2023

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.
Keywords: Multi-agent system, robust control, portfolio optimization, financial application

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.

Keywords: Multi-agent system, robust control, portfolio optimization, financial application