Optimal portfolio selection with liability management and Markov switching under constrained variance

In this paper, we mainly discuss an optimal portfolio selection model with liability management and Markov switching which maximize the expected final surplus under constrained variance. Because linear quadratic control is a basic method for the M–VM–V problem, in this paper we begin with the general stochastic linear quadratic model, and obtain the optimal solution of the problem. Exactly, the analytical optimal portfolio strategy is derived in this paper. Furthermore, we demonstrate that a special case is consistent with those results of Chiu and Li (2006) [3].