chebyshev wavelet-based method or solving stochastic optimal controlproblems and its application in finance

In this paper, a computational method based on parameterizing state andcontrol variables is presented for solving stochastic optimal control(soc) problems.by using chebyshev wavelets with unknown coeffcients, state and control variables areparameterized, and then a stochastic optimal control problem is converted to a stochastic optimization problem.the expected cost functional of the resulting so problem isapproximated by sample average approximation (saa), thereby the problem is formulated as a deterministic optimal control problem which can be solved by optimizationmethods, more easily. for guaranteeing convergence of the presented method a newtheorem is proved. finally, the proposed method is implemented for solving mertonportolio allocation problem in finite horizon. the simulation results illustrate improvement of constructed portfolio return.