Reflected BSDEs with regulated trajectories

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e. trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the solution corresponds to the value of an optimal stopping problem and may be approximated by a modified penalization method.     

BSDEs with random default time and related zero-sum stochastic differential games

In this Note we are concerned with backward stochastic differential equations with random default time. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions and a comparison theorem for their solutions. As an application, we get a saddle-point strategy for the related zero-sum stochastic differential game problem.     

Comparison theorems for anticipated BSDEs with non-Lipschitz coefficients

We study comparison theorems for one dimensional anticipated backward stochastic differential equations under one kind of non-Lipschitz assumption. In the results, the generator functions are allowed to contain the anticipated term of z, neither generator function needs to be necessarily monotone in the anticipated term of y  , and the anticipated times of the anticipated terms of (y,z)$(y,z)$ in one generator function can differ from those in the other.     

反射型的带跳倒向双重随机微分方程

证明了反射型的带跳倒向双重随机微分方程的解的存在唯一性.主要方法是Snell包和不动点定理.     

一类新的线性二次随机最优控制器的设计

给出一类正倒向随机微分方程解的存在唯一性结果,应用这个结果研究了一类新的推广的随机线性二次最优控制器的设计问题,得到了由正倒向随机微分方程解所表示的唯一最优控制器的显式结构;在推广的Riccati方程系统基础上,得到最优控制器精确的线性反馈形式.最后,给出了随机线性二次最优控制器的设计算法.     

Representation theorems for generators of BSDEs in L p spaces

In this paper,we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t,y,z),when the terminal data is in L p spaces,for 1 < p ≤ 2.     

RBSDE''''s with jumps and the related obstacle problems for integral-partial differential equations

The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.     

倒向随机微分方程的一个一般的反比较定理

在由彭实戈引入的倒向随机微分方程的最基本的条件下,提出并证明了一个一般的反比较定理.     

z一致连续的倒向随机微分方程解的一个存在唯一性结果

建立了关于一维倒向随机微分方程(简写为BSDE)的一个存在唯一性结果,其中BSDE的生成元g关于y满足Constantin条件,关于z是一致连续的.这改进了一些已知结果.     

RBSDE’s with jumps and the related obstacle problems for integral-partial differential equations

The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.     

带跳的分数倒向重随机微分方程及相应的随机积分偏微分方程

本文首次把Poisson随机测度引入分数倒向重随机微分方程,基于可料的Girsanov变换证明由Brown运动、Poisson随机测度和Hurst参数在(1/2,1)范围内的分数Brown运动共同驱动的半线性倒向重随机微分方程解的存在唯一性.在此基础上,本文定义一类半线性随机积分偏微分方程的随机黏性解,并证明该黏性解由带跳分数倒向重随机微分方程的解唯一地给出,对经典的黏性解理论作出有益的补充.     

A maximum principle for optimal control problems with mixed constraints

Necessary conditions in the form of maximum principles are derivedfor optimal control problems with mixed control and state constraints.Traditionally, necessary condtions for problems with mixed constraintshave been proved under hypothesis which include the requirementthat the Jacobian of the mixed constraint functional, with respectto the control variable, have full rank. We show that it canbe replaced by a weaker ‘interiority’ hypothesis.This refinement broadens the scope of the optimality conditions,to cover some optimal control problems involving differentialalgebraic constraints, with index greater than unity.     

Anticipated BSDEs driven by a single jump process

In this paper, we discuss a class of anticipated backward stochastic differential equations related to a finite continuous time single jump process. We prove the existence and uniqueness of the adapted solution. Moreover, a comparison theorem for the solutions is also established.     

BSDEs and SDEs with time-advanced and -delayed coefficients

ABSTRACT

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established.     

具有一致连续生成元和可积参数的倒向随机微分方程

本文建立了具有可积参数的一维倒向随机微分方程(BSDE) 的一个新的存在唯一性结果, 其中BSDE 的生成元g 关于y 满足Osgood 条件且关于z 是α-Hölder (0 < α < 1) 连续的.