Local Strict Comparison Theorem and Converse Comparison Theorems for Reflected Backward Stochastic Differential Equations

Representation theorems for generators of Reflected BSDEs with continuous and linear-growth generators

In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDE), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDE). As some applications, a general converse comparison theorem for RBSDE is obtained and some properties of RBSDE are discussed.

反射随机微分方程的最优控制问题：存在性

Optimal control problem for reflected stochastic differential equation: existence

本文研究了反射随机微分方程驱动系统的最优控制存在性，通过弱收敛技术和Skorokhod定理证明了广义和严格最优控制的存在性。

带泊松跳的反射McKean-Vlasov随机微分方程的最优控制问题

Optimal control problem for reflected McKean--Vlasov stochastic differential equations with Poisson jumps

针对一类带泊松跳的一维反射McKean-Vlasov随机微分方程，利用Aldous紧性准则和Skorokhod映射连续性，证明了最优松弛控制的存在性，并在Roxin凸性条件下得到严格最优控制的存在性。

One dimensional reflected BSDEs with two barriers under logarithmic growth and applications

In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a logarithmic growth $(|y||\ln|y||+|z|\sqrt{|\ln|z||})$ in the state variables $y$ and $z$. The terminal value $ξ$ and the obstacle processes $(L_t)_{0\leq t\leq T}$ and $(U_t)_{0\leq t\leq T}$ are $L^p$-integrable for a suitable $p > 2$. The main idea is to use the concept of local solution to construct the global one. As applications, we broaden the class of functio…

布朗滤波初始放大下的倒向随机微分方程与反射倒向随机微分方程

Backward and reflected backward stochastic differential equations under initial enlargement of Brownian filtrations

该研究探讨布朗滤波初始放大对BSDEs和RBSDEs的影响，建立相关表示性质与恒等式，通过反例说明奇异方程解的唯一性问题，发展正则BSDE的条件参数化并讨论扩展方向。