A new ensemble Monte Carlo method for a parabolic optimal control problem with random coefficient

A new ensemble Monte Carlo (EMC) method is proposed and applied to numerically simulate a parabolic optimal control problem with random coefficients. The state equation is discretized by the EMC method, which shares a common coefficient matrix with multiple right-hand vectors. It saves the computational cost compared with the Monte Carlo (MC) method. For this new EMC method, it is unconditionally stable and does not need to subgroup the samples in the simulation. Under natural regularity condition, some error estimates are obtained for the EMC approximation of the optimal control problem. Two numerical examples are presented to test the theoretical results.