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Stochastic-fractional optimal control problems and application in portfolio management | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 4، شماره 2، اسفند 2024، صفحه 99-114 اصل مقاله (706.36 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.82579.1151 | ||
| نویسندگان | ||
| Saba Yaghobipour* 1؛ Majid Yarahmadi2 | ||
| 1Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran. | ||
| 2Department of Mathematics and Computer Science, Lorestan University, Lorestan 68151-44316, Iran. | ||
| چکیده | ||
| The aim of this paper is to propose a new method for solving a calss of stochasticfractional optimal control problems. To this end, we introduce an equivalent form for the presented stochastic-fractional optimal control problem and prove that these problems have the same solution. Therefore, the corresponding Hamilton– Jacobi–Bellman (HJB) equation to the equivalent stochastic-fractional optimal control problem is presented and then the Hamiltonian of the system is obtained. Finally, by considering Sharpe ratio as a performance index, Merton’s portfolio selection problem is solved by the presented stochastic-fractional optimal control method. Moreover, for indicating the advantages of the proposed method, optimal pairs trading problem is simulated. | ||
| کلیدواژهها | ||
| Stochastic fractional function؛ Sharpe ratio؛ Optimal control؛ Portfolio management | ||
| مراجع | ||
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