Chebyshev wavelet-based method for solving various stochastic optimal control problems and its application in finance

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 شهریور 1402

نوع مقاله: 5NSCO-2023

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.82445.1265

نویسندگان

Majid Yarahmadi^* ؛ Saba Yaghobipour

Department of Mathematics and Computer Sciences, Lorestan University, Lorestan, Iran.

چکیده

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 coefficients, 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 the Sample Average
Approximation (SAA), thereby the problem can be solved by optimization methods, more easily. For facilitating and
guaranteeing convergence of the presented method a new theorem is proved. Finally, the proposed method is implemented,  based on a newly designed algorithm for solving one of the well-known problems in mathematical finance, the Merton portfolio allocation problem in finite horizon. The simulation results illustrate the improvement of the constructed portfolio return.

کلیدواژه‌ها

Stochastic optimal control؛ Chebyshev wavelets؛ Expansion؛ Optimal