A Markovian regime-switching stochastic differential game for portfolio risk minimization

Abstract

A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state Markov chain. We interpret the states of the chain as different market regimes. A convex risk measure is used as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero- sum stochastic differential game. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided.