Game-theoretic approach to risk-sensitive benchmarked asset management

Article type: Research Article

Authors: Deshpande, Amogh^{; ;} | Jacka, Saul

Affiliations: Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. E-mail: [email protected] | Department of Statistics, University of Warwick, Coventry, UK. E-mail: [email protected]

Note: [] Address for correspondence: Amogh Deshpande, Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. E-mail: [email protected]

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

DOI: 10.3233/RDA-140108

Journal: Risk and Decision Analysis, vol. 5, no. 4, pp. 163-176, 2014