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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 | ||
آمار تعداد مشاهده مقاله: 16 |