近期，吴付科教授团队的文章《Systems of Singularly Perturbed Forward-Backward Stochastic Differential Equations and Control Problems》在国际期刊《SIAM Journal on Control and Optimization》发表。

      摘要：This paper focuses on systems of singularly perturbed forward-backward stochastic differential equations (FBSDEs) and control problems. Assuming Lipschitz continuity on the coefficients and allowing degeneracy in the diffusion terms, the solution of a two-time-scale FBSDE is shown to converge to the solution of an averaged FBSDE as a small parameter \(\varepsilon\) tending to zero. Moreover, it is shown that the value function of the singularly perturbed systems converges to the solution of a nonlinear partial differential equation (PDE). Furthermore, under additional conditions, it is demonstrated that the solution of the limit PDE is in fact the limit value function. These results provide insights into the convergence rate and extend existing results on the averaging principles for such stochastic control problems.

      论文链接：https://epubs.siam.org/doi/10.1137/25M1755084