Mean variance optimal control of Markov jump with multiplicative noise systems

In this paper we consider the mean variance stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is to minimize the final variance subject to a restriction on the final expected value of the output, or to maximize the final expected value subject to a restriction on the final variance of the output of the system. We also consider the performance criterion composed by a linear combination of the final variance and expected value of the output of the system. The optimal control strategies are obtained from a set of interconnected Riccati difference equations. Additionally, we formulate an asset liabilities management model for defined-benefit pension funds with regime switching using our model. We assume in this case that the market parameters depend on the market mode that switches according to a Markov chain among a finite number of states.