Allameh Tabataba'i University Press Journal of Mathematics and Modeling in Finance 2783-0578 4 2 2024 12 01 Stochastic-fractional optimal control problems and application in portfolio management 99 114 18191 10.22054/jmmf.2024.82579.1151 EN Saba Yaghobipour Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran. Majid Yarahmadi Department of Mathematics and Computer Science, Lorestan University, Lorestan 68151-44316, Iran. Journal Article 2024 10 23 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. https://jmmf.atu.ac.ir/article_18191_cb4531642293dd3dde3e6351ec5f4d95.pdf