Discussion Papers 2021

CIRJE-F-1173	"Equilibrium Multi-Agent Model with Heterogeneous Views on Fundamental Risks"
Author Name	Kizaki, Keisuke, Taiga Saito and Akihiko Takahashi
Date	July 2021
Full Paper	PDF file
Remarks	Revised in August, September, December 2021 and August, October 2023; forthcoming in Automatica.

Abstract
This paper investigates an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating uncer- tainties 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 con- sumption 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.
Keywords: Stochastic control; Optimization under uncertainties; Interest rate model; Application in nance

Abstract

This paper investigates an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating uncer- tainties 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 con- sumption 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.

Keywords: Stochastic control; Optimization under uncertainties; Interest rate model; Application in nance