A risk-sensitive maximum principle for a Markov regime-switching jump-diffusion system and applications

¹ School of Mathematics, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
² Actuarial Science Program, Department of Mathematics, Morgan State University, Maryland 21251, USA
elisabeth.brown@morgan.edu
³ African Institute for Mathematical Sciences, University of Ghana, Ghana
⁴ Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, L69 7ZL, United Kingdom
menoukeu@liv.ac.uk

^a Corresponding author: zysun_nk@126.com

Received: 18 July 2016
Revised: 8 March 2017
Accepted: 21 May 2017

Abstract

In this paper, we derive a general stochastic maximum principle for a risk-sensitive type optimal control problem of Markov regime-switching jump-diffusion model. The results are obtained via a logarithmic transformation and the relationship between adjoint variables and the value function. We apply the results to study both a linear-quadratic optimal control problem and a risk-sensitive benchmarked asset management problem for Markov regime-switching models. In the latter case, the optimal control is of feedback form and is given in terms of solutions to a Markov regime-switching Riccatti equation and an ordinary Markov regime-switching differential equation.