论文标题
广义BSDE和反映广义BSDE的适应性和惩罚方案
Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs
论文作者
论文摘要
该论文是在一般危险过程设置中对脆弱的欧洲和美国选择的定价以及对相应违约前后随机微分方程（BSDE）和前默认前反映向后随机微分方程（RBSDE）的相关研究的动机。我们使用通用过滤$ \ ff $，假定Martingale代表财产相对于正方形的Martingale $ m $，而这项工作的目标是双重的。首先，我们旨在为广义BSDE和反射的广义BSDE建立良好的结果和比较定理，并具有连续且非抵押的驾驶员$ a $ a $。其次，我们研究了广义BSDE和反射的广义BSDE的扩展惩罚计划，在该计划中，我们对驾驶员进行惩罚，以便在限制中获得特定的最佳停止问题或dynkin游戏，其中一组可接受的运动时间被限制在$ a $ a $ a $ a $ a $ a $ a $ a的正确支持下。
The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and pre-default reflected backward stochastic differential equations (RBSDE). We work with a generic filtration $\FF$ for which the martingale representation property is assumed to hold with respect to a square-integrable martingale $M$ and the goal of this work is of twofold. First, we aim to establish the well-posedness results and comparison theorems for a generalized BSDE and a reflected generalized BSDE with a continuous and nondecreasing driver $A$. Second, we study extended penalization schemes for a generalized BSDE and a reflected generalized BSDE in which we penalize against the driver in order to obtain in the limit either a particular optimal stopping problem or a Dynkin game in which the set of admissible exercise time is constrained to the right support of the measure generated by $A$.
