Document Type : Research Article
Authors
1 Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran.
2 Department of Mathematics and Computer Science, Lorestan University, Lorestan 68151-44316, Iran.
Abstract
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.
Keywords
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