Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality

We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.

随机变分不等式的二阶微分方程方法

运用具有正黏性阻尼系数和时间尺度系数的二阶微分方程系统来求解随机变分不等式问题(stochastic variational inequality problem,SVIP)。首先,应用互补函数和样本均值近似(sample average approximation,SAA)方法对原始问题进行等价转换,即将随机变分不等式问题转化为一个方程组,在此基础上建立具有正黏性阻尼系数γ(t)和时间尺度系数β(t)的二阶微分方程系统;其次,研究了该二阶微分方程系统轨迹的收敛性和收敛速率;最后,给出两个数值实验说明该二阶微分方程系统求解随机变分不等式问题的有效性。

汇率的混合经典脉冲控制——非对称因素和多边关系因素

该文在AbelCadenillast与FernandoZapatero关于汇率控制的基本框架下,对汇率的混合经典-脉冲控制模型作了改进.其一是考虑了汇率变化对多边关系所产生的不同影响;其二是考虑到汇率高于或低于目标时对经济造成的影响是非对称的;其三是考虑到较高的利率与较低的利率对经济的影响也是非对称的.文章对新模型进行了分析,得出了求简单控制策略的非线性常微分方程,并对其中只考虑随机脉冲控制的情况导出了解析解的形式,给出了充分性的条件.

带Lévy过程的正倒向对偶系统随机控制问题

讨论了一类控制系统是带Lévy过程的正倒向对偶随机微分方程的随机控制问题.本文假定控制区域为凸集,最优解是使目标函数达到最小的控制过程.使用带Lévy过程的Ito公式及Ekeland变分原理,作者建立了这类随机控制问题极值原理的一个必要条件.

一类随机微分变分不等式

在一定条件下证明随机微分变分不等式解的存在性与唯一性.首先,证明随机微分变分不等式等价于随机投影系统;其次,用压缩映射原理证明该系统的解的存在性与唯一性;最后,考虑含参的随机微分变分不等式,并证明在一定条件下其解的稳定性.

中央银行干预外汇交换市场的最优策略

现汇的交换率服从几何布朗运动。中央银行的目的是使交换率尽可能限制在一个给定区域。在交换率与给定目标之间有消费成本。另外，在每一次干预中，存在一个固定成本和比例成本。目的是找一个最优干预水平和规模，使得总成本最小。可以用随机脉冲控制来解决这一问题。

Optimal vaccination strategy for a mean-field stochastic susceptible-infected-vaccinated system

The parameters of biological system may change under the influence of different states or state processes.The change of parameters can also affect the dynamic behaviors of epidemic disease.This paper presents a mean field stochastic susceptible-infectedvaccinated(SIV)epidemic model which parameters depend on the state process.The sufficient and necessary conditions of optimal control of the novel epidemic model are obtained by maximum principle.Finally,we perform representative numerical simulations to illustrate the theoretical results and further discuss the feasibility based on the hand,foot and mouth disease(HFMD)data in China.

Indifference pricing and hedging in a multiple-priors model with trading constraints

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.

Peng's maximum principle for a stochastic control problem driven by a fractional and a standard Brownian motion

We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.