Game-theoretic approach to risk-sensitive benchmarked asset management

TL;DR

This paper models a risk-sensitive asset management problem as a stochastic differential game between an investor and the market, deriving explicit optimal strategies for both players.

Contribution

It introduces a game-theoretic framework for risk-sensitive benchmarked asset management and provides explicit solutions for the optimal strategies of both market and investor.

Findings

Explicit optimal strategies for both players derived

Game-theoretic model captures market and investor interactions

Analytical solutions enhance understanding of risk-sensitive asset management

Abstract

In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market which tries to minimize the expected payoff of the investor. The market does this by modulating a stochastic benchmark that the investor needs to outperform. We obtain an explicit expression for the optimal pair of strategies as for both the players.