Lévy过程驱动的BSDE的反比较定理与Jensen不等式（英文）

本文研究了由一维Lévy过程驱动的倒向随机微分方程(BSDE)的反比较定理.利用一般g-期望下BSDE的反比较定理的证明方法,推导出了一般f-期望下BSDE的反比较定理,并给出了一般f-期望下Jensen不等式成立的充分必要条件.     

部分信息下资产收益率发生紊乱的最优投资策略

本文研究了在部分信息且市场利率非零的情形下,资产预期收益率发生紊乱(disorder)时,终端净财富的期望指数效用最大化问题.利用半鞅和倒向随机微分方程(BSDE)刻画价值过程的方法,获得了最优交易策略和价值过程的明确表达式,推广了一般框架下最优投资组合的研究结果.     

Lévy过程驱动的BSDE的反比较定理与Jensen不等式

本文研究了由一维Lévy过程驱动的倒向随机微分方程(BSDE)的反比较定理.利用一般g-期望下BSDE的反比较定理的证明方法,推导出了一般f-期望下BSDE的反比较定理,并给出了一般f-期望下Jensen不等式成立的充分必要条件.     

L′evy 过程驱动的BSDE的反比较定理与Jensen不等式

本文研究了由一维L′evy过程驱动的倒向随机微分方程（BSDE）的反比较定理。利用一般g -期望下BSDE的反比较定理的证明方法,推导出了一般f -期望下BSDE的反比较定理,并给出了一般f -期望下Jensen不等式成立的充分必要条件。     

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.     

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.     

随机Lipschitz条件下一般时间终端的多维BSDE解的存在唯一性

某个新的范数空间上利用压缩映像原理,在生成元g满足对二元组■均不一致的随机Lipschitz条件下,证明了一般时间终端多维倒向随机微分方程(BSDE)解的存在唯一性,作为推论得到了该类倒向随机微分方程解的递归迭代序列的收敛性.     

带有随机生成元的倒向随机微分方程的共单调定理

该文利用Malliavin微分的方法研究带有随机生成元的倒向随机微分方程 (简记BSDE),给出了关于比较某些BSDE的解(y,z)中z的方法, 在此基础上继续研究(y,z)的某些重要性质, 指明了当BSDE的生成元是随机的情况下,Zengjing Chen等人文章中得到的共单调定理是不成立的, 然后寻找带有随机生成元的BSDE的共单调定理成立的特殊情况, 最后研究了一类g -期望的可加性以及Choquet积分表示定理.     

关于（y,z）限制的BSDE解

本文讨论漂移系数g（S,·,·）不满足Lipschitz条件的一类例向随机微机方程（BSDE）关于（x,y）限制条件下最小g-上解的存在唯一性,为此我们讨论了这一类BSDE的比较定理．推广了[1]在g（s,·,·）关于（x,y）满足Lipschitz条件下的结果．     

系数为左Lipschitz的倒向随机微分方程解的存在性

考虑一类一维倒向随机微分方程(BSDE),其系数关于y满足左Lipschitz条件(可能是不连续的),关于z满足Lipschitz条件.在这样的条件下,证明了BSDE的解是存在的,并且得到了相应的比较定理.     

Reflected mean-field backward stochastic differential equations. Approximation and associated nonlinear PDEs

Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely probabilistic method, to characterize its limit which is the solution of mean-field backward stochastic differential equations (BSDEs) with reflections. On the other hand, we will prove that this type of reflected mean-field BSDEs can also be obtained as the limit equation of the mean-field BSDEs by penalization method. Finally, we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean-field BSDEs.     

Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob–Meyer decomposition of Peng to a general context.     

关于倒向随机微分方程生成元的逆比较定理

Coquet等人在g(t,y ,0 )≡ 0的条件下建立了一个关于倒向随机微分方程生成元g的逆比较定理 .本文对一般的倒向随机微分方程的生成元以及对L2 有界的生成元分别得到了两个新的逆比较定理 .     

One-dimensional BSDEs with finite and infinite time horizons

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators.     

BSDEs with Jumps and Path-Dependent Parabolic Integro-differential Equations

This paper deals with backward stochastic differential equations with jumps, whose data (the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.     

Reflected BSDEs with nonpositive jumps,and controller-and-stopper games

We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization approach under regularity assumptions on the obstacle. In a suitable regime switching diffusion framework, we show the connection between our class of BSDEs and fully nonlinear variational inequalities. Our BSDE representation provides in particular a Feynman–Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affects both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this BSDE minimal solution involving equivalent change of probability measures, and discount processes. This gives in particular a new representation for zero-sum stochastic differential controller-and-stopper games.     

BSDEs driven by time-changed Lévy noises and optimal control

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally appear in control problems. Here we prove a sufficient maximum principle for a general optimal control problem of a system driven by a time-changed Lévy noise. As an illustration we solve the mean–variance portfolio selection problem.     

Invariant Representation for Stochastic Differential Operator by Bsdes with Uniformly Continuous Coefficients and its Applications

In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.     

Density analysis of non-Markovian BSDEs and applications to biology and finance

In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance.     

Mean-Field Backward Stochastic Differential Equations Driven by Fractional Brownian Motion

In this paper, we study a new class of equations called mean-field backward stochastic differential equations(BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H 1/2. First, the existence and uniqueness of this class of BSDEs are obtained. Second, a comparison theorem of the solutions is established. Third, as an application, we connect this class of BSDEs with a nonlocal partial differential equation(PDE, for short), and derive a relationship between the fractional mean-field BSDEs and PDEs.