Affiliations: Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. E-mail: addeshpa@gmail.com | Department of Statistics, University of Warwick, Coventry, UK. E-mail: S.D.Jacka@warwick.ac.uk
Note: [] Address for correspondence: Amogh Deshpande, Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. E-mail: addeshpa@gmail.com
Abstract: In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo [Quantitative Finance 8(4) (2008), 415–426]. 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.
Keywords: Risk-sensitive control, zero sum stochastic differential game
