An efficient algorithm for stochastic optimal control problems by means of a least-squares Monte-Carlo method. (2nd November 2022) - Öz Bakan, Hacer; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm
Abstract : In this work, we provide discrete optimality conditions of the optimal control problems of stochastic differential equations. Euler and Runge–Kutta methods are used for discretization. A Lagrange multiplier method for a discrete-time stochastic optimal control problem is formulated. The discrete adjoint process p n is obtained in terms of conditional expectations E [ p n + 1 ] and E [ p n + 1 Δ W ] for both methods. To estimate these nested conditional expectations at each time step via simulation, we use a very powerful new approach, least-squares Monte-Carlo method, developed by Longstaff–Schwartz. This is the first time to solve a stochastic optimal control problem by calculating the nested conditional expectations numerically with the help of a least-squares Monte-Carlo method. Some examples are studied to test and demonstrate the efficiency of the Lagrange multiplier combined with the least-squares Monte-Carlo method.