The Stochastic LQ Framework with Markov Modulation Parameters

This paper studies a stochastic linear-quadratic (LQ) framework over a continuous-time stationary state with Markovian jumps in parameter values, allowing the weighting parameters to be limited. In order to fully consider the influence of the state factors in the classical stochastic LQ control problem, the control model is extended to a jump-diffusion model in this paper. By introducing a jump-diffusion stochastic Riccati equation and applying random variational method, the optimal feedback control strategy of the new model is obtained. As applications, the new stochastic LQ control model proves to be an effective framework to solve the optimal portfolio selection problem and the hedging strategy problem in finance in the light of the recent development on general stochastic LQ problems.