有限时区上的最优转换和停止问题

讨论了有限时区上的最优转换和停止问题,它是一类同时具备脉冲控制和最优停止特征的最优控制问题.问题的最优值以及最优转换和停止决策可以由具有混合障碍的多维反射倒向随机微分方程的解来刻画.接着考虑了形式更一般的反射倒向随机微分方程并证明了方程解的存在唯一性.     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Mémin,Peng[1],Coquet,Hu,Mémin,Peng[2],Chen[3],Jiang[8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题.在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题.本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题.     

随机递归最优控制和混合最优控制问题

对随机递归最优控制问题即代价函数由特定倒向随机微分方程解来描述和递归混合最优控制问题即控制者还需 决定最优停止时刻, 得到了最优控制的存在性结果. 在一类等价概率测度集中,还给出了递归最优值函数的最小和最大数学期望.     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

关于反射倒向随机微分方程的解的一些性质(英文)

研究了关于反射倒向随机微分方程的解的一些性质.同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理.     

生成元连续且线性增长的反射倒向随机微分方程生成元的表示定理（英文）

本文建立了一个生成元满足连续且线性增长条件的反射倒向随机微分方程生成元的局部表示定理,此定理推广了一些已有的倒向随机微分方程生成元的表示定理.应用此表示定理,本文获得了一个一般的反射倒向随机微分方程的逆比较定理,同时讨论了此类方程的一些性质.     

关于反射倒向随机微分方程的解的一些性质

研究了关于反射倒向随机微分方程的解的一些性质．同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理．     

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.     

Knight不确定下考虑保险和退休的最优消费-投资和遗产问题研究

研究在Knight不确定环境下,考虑投资者遗产和保险,在三种不同借款约束下的最优消费与投资问题.借助于倒向随机微分方程（BsDE）理论求出了投资者最优消费和投资策略的显式表达式.最后结合数值分析,给出含糊与含糊态度对最优消费和投资决策的影响.     

带跳反射倒向随机微分方程与相应的 积分-偏微分方程障碍问题

证明由 Brown 运动和 Poisson 随机测度共同驱动的终端为停时的反射倒向随机微分方程存在唯一解,并且在 Markov框架下该解为积分-偏微分方程障碍问题黏性解提供了概率解释.     

Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps

We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). The financial position is given by an RCLL adapted process. We first state some properties of RBSDEs with jumps when the obstacle process is RCLL only. We then prove that the value function of the optimal stopping problem is characterized as the solution of an RBSDE. The existence of optimal stopping times is obtained when the obstacle is left-upper semi-continuous along stopping times. Finally, we investigate robust optimal stopping problems related to the case with model ambiguity and their links with mixed control/optimal stopping game problems. We prove that, under some hypothesis, the value function is equal to the solution of an RBSDE. We then study the existence of saddle points when the obstacle is left-upper semi-continuous along stopping times.     

Switching problem and related system of reflected backward SDEs

This paper studies a system of backward stochastic differential equations with oblique reflections (RBSDEs for short), motivated by the switching problem under Knightian uncertainty and recursive utilities. The main feature of our system is that its components are interconnected through both the generators and the obstacles. We prove existence, uniqueness, and stability of the solution of the RBSDE, and give the expression of the price and the optimal strategy for the original switching problem via a verification theorem.     

A Bayesian-martingale approach to the general disorder problem

We consider a Bayesian-martingale approach to the general change-point detection problem. In our setting the change-point represents a random time of bifurcation of two probability measures given on the space of right-continuous functions. We derive a reflecting backward stochastic differential equation (RBSDE) for the value process related to the disorder problem and show that in classical cases of the Wiener and Poisson disorder problems this RBSDE is equivalent to free-boundary problems for parabolic differential and differential–difference operators respectively.     

Reflected Backward Stochastic Differential Equations,Convex Risk Measures and American Options

We use convex risk measures to assess unhedged risks for American-style contingent claims in a continuous-time non-Markovian economy using reflected backward stochastic differential equations (RBSDEs). A two-stage approach is adopted to evaluate the risk. We formulate the evaluation problem as an optimal stopping-control problem and discuss the problem using reflected BSDEs. The convex risk measures are represented as solutions of RBSDEs. In the Markov case, we relate the RBSDE solutions to the unique viscosity solutions of related obstacle problems for parabolic partial differential equations.     

Optimal control of random evolutions

We consider a stochastic control problem for a random evolution. We study the Bellman equation of the problem and we prove the existence of an optimal stochastic control which is Markovian. This problem enables us to approximate the general problem of the optimal control of solutions of stochastic differential equations.     

The Filtering Equations of Forward-Backward Stochastic Systems with Random Jumps and Applications to Partial Information Stochastic Optimal Control

In this article, we consider a filtering problem for forward-backward stochastic systems that are driven by Brownian motions and Poisson processes. This kind of filtering problem arises from the study of partially observable stochastic linear-quadratic control problems. Combining forward-backward stochastic differential equation theory with certain classical filtering techniques, the desired filtering equation is established. To illustrate the filtering theory, the theoretical result is applied to solve a partially observable linear-quadratic control problem, where an explicit observable optimal control is determined by the optimal filtering estimation.     

Continuity Properties of Optimal Multiple Stopping Value

This article is concerned with the optimal multiple stopping problem for discrete time finite stage stochastic processes. We study lower semicontinuity and continuity properties of optimal stopping values with respect to the topology of convergence in distribution. Also, we formulate the multiple stopping version of the prophet inequality for the optimal stopping problem and apply the lower semicontinuity property of optimal stopping values to the prophet inequality for the optimal multiple stopping problem.     

Optimal stopping of switching diffusions with state dependent switching rates

This paper is concerned with a continuous-time and infinite-horizon optimal stopping problem in switching diffusion models. In contrast to the assumption commonly made in the literature that the regime-switching is modeled by an independent Markov chain, we consider in this paper the case of state-dependent regime-switching. The Hamilton–Jacobi–Bellman (HJB) equation associated with the optimal stopping problem is given by a system of coupled variational inequalities. By means of the dynamic programming (DP) principle, we prove that the value function is the unique viscosity solution of the HJB system. As an interesting application in mathematical finance, we examine the problem of pricing perpetual American put options with state-dependent regime-switching. A numerical procedure is developed based on the DP approach and an efficient discrete tree approximation of the continuous asset price process. Numerical results are reported.