A New Method for Solving Merton Problem in an Infinite Horizon

In classical methods for solving infinite horizon stochastic optimal control problems (SOCPs), the main attempts are focused to determine the solution by introducing the value function via dynamic programming and Hamilton-Jacobi-Bellman equation. But in general, determination of solution in a closed form is not simple. For this necessity and to find of an appropriate optimal trajectory and control, in this article, we introduce a hybrid method to solve a class of SOCPs. This new approach is combined of stochastic differential transform method (SDTM) and approximation method of infinite horizon context via finite horizon. An applicable example in economical science is also presented to show the ability and efficiency of the presented method.