Chebyshev wavelet-based method or solving Stochastic Optimal Control Problems and its Application in Finance

In this paper, a computational method based on parameterizing state and control variables is presented for solving Stochastic Optimal Control(SOC) problems. By using Chebyshev wavelets with unknown coeffcients, state and control variables are parameterized, and then a stochastic optimal control problem is converted to a stochastic optimization problem.The expected cost functional of the resulting SO problem is approximated by Sample average approximation (SAA), thereby the problem is formulated as a deterministic optimal control problem which can be solved by optimization methods, more easily. For guaranteeing convergence of the presented method a new theorem is proved. Finally, the proposed method is implemented for solving Merton portolio allocation problem in finite horizon. The simulation results illustrate improvement of constructed portfolio return.