Stochastic-fractional optimal control problems and application in portfolio management

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.