Switching problems with controlled randomisation and associated obliquely reflected BSDEs

Switching Game of Backward Stochastic Differential Equations and Associated System of Obliquely Reflected Backward Stochastic Differential Equations

This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the penalization method, the monotone convergence, and the a priori estimates.

Obliquely Reflected BSDEs

In this paper, we study existence and uniqueness to multidimensional Reflected Backward Stochastic Differential Equation in an open convex domain, allowing for oblique directions of reflection. In a Markovian framework, combining \emph{a priori} estimates for penalised equations and compactness arguments, we obtain existence results under quite weak assumptions on the driver of the BSDEs and the direction of reflection, which is allowed to depend on both $Y$ and $Z$. In a non Markovian framework, we obtain existence and uniqueness result for direction of reflection depending on time and $Y$. W…

Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems

In this paper, we prove new convergence results improving the ones by Chassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs, arising in the study of switching problems, were considered by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89--121] and generalized by Hamadène and Zhang [Stochastic Process. Appl. 120 (2010) 403--426] and Chassagneux, Elie and Kharroubi [Electron. Commun. Probab. 16 (2011) 120--128]. Our main result is a rate of convergence obtained in the Lipschit…

关于具有随机Lipschitz系数的无限时域反射倒向随机微分方程的一个注记

A Note on Reflected BSDEs in Infinite Horizon with Stochastic Lipschitz Coefficients

本文将无限时域反射BSDE的结果推广到生成元具有随机Lipschitz系数的情形，并将其应用于生成元线性增长的FSDE稳健最优停止问题。

带公共噪声的平均场控制问题的随机化方法

A randomisation method for mean-field control problems with common noise

本文提出一种控制随机化方法，将带公共噪声的平均场控制问题转化为控制泊松点过程强度的问题，并通过BSDE和随机化动态规划原理刻画值函数。