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

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 14، Issue 1 - شماره پیاپی 28، خرداد 2024، صفحه 1-19   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.82445.1265

نویسندگان

M. Yarahmadi^* ؛ S. 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 stochastic optimization problem is approximated by sample average approximation thereby the problem can be solved by optimization methods more easily. For facilitating and guar-anteeing 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 fi-nance, the Merton portfolio allocation problem in finite horizon. The simu-lation results illustrate the improvement of the constructed portfolio return.

کلیدواژه‌ها

Stochastic optimal control؛ Chebyshev wavelets؛ Expansion؛ Optimal asset allocation

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