Time-Reversal of Stochastic Maximum Principle
CoRR(2024)
摘要
Stochastic maximum principle (SMP) specifies a necessary condition for the
solution of a stochastic optimal control problem. The condition involves a
coupled system of forward and backward stochastic differential equations
(FBSDE) for the state and the adjoint processes. Numerical solution of the
FBSDE is challenging because the boundary condition of the adjoint process is
specified at the terminal time, while the solution should be adaptable to the
forward in time filtration of a Wiener process. In this paper, a
"time-reversal" of the FBSDE system is proposed that involves integration with
respect to a backward in time Wiener process. The time-reversal is used to
propose an iterative Monte-Carlo procedure to solves the FBSDE system and its
time-reversal simultaneously. The procedure involves approximating the
Föllmer's drift and solving a regression problem between the state and its
adjoint at each time. The procedure is illustrated for the linear quadratic
(LQ) optimal control problem with a numerical example.
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