Continuous-time Markov Decision Processes In Random Environments

This paper mainly studies the optimal control of continuous-time Markov decision processes in a random environment.First,we give some conditions to prove the existence of optimal control strategy under a finite-horizon cri-terion;based on this result,further we add random environment impacts to give the existence of optimal Markov control;then we substantiate the con-tinuity of the value function;finally,we study the optimal investment policy of the Merton investment model.