Journal of Optimization Theory and Applications, vol.202, no.1, pp.497-517, 2024 (SCI-Expanded)
In this work, we obtain weak order-2 conditions of Runge–Kutta method for the optimal control of stochastic differential equations which occurs in many areas of economics and finance and recently in cognitive sciences and neuroscience. We get the order conditions that a stochastic Runge–Kutta technique must meet to have weak order two by comparing the stochastic expansion of the approximation with the associated Taylor scheme. Moreover, we present numerical examples which verify the theoretical results. We conclude our paper by a summary and an outlook to future research and application.