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.