基于g-期望的部分可观测非零和随机微分博弈（英文）

本文研究了g-期望下的部分可观测非零和随机微分博弈系统,该系统的状态方程由It?-Lévy过程驱动,成本函数由g-期望描述.根据Girsanov定理和凸变分技巧,本文得到了最大值原理和验证定理.为对所获结果进行说明,本文讨论了关于资产负债管理的博弈问题.     

面向容侵系统可生存性量化的随机博弈模型研究

提出面向生存性研究的容侵系统状态转换模型,提高对容侵过程的描述能力,将入侵者和入侵容忍系统作为随机博弈的局中人,建立了描述入侵过程的随机博弈模型,使用纳什均衡计算了博弈结果,使用基于连续马尔可夫过程的方法对容侵系统可生存性进行了量化评估.最后,利用博弈分析的结果和所建立的评估模型进行了容侵系统的生存性分析,指出了容侵系统生存性敏感的参数.     

多模态It随机系统的均方稳定性与鲁棒镇定

研究由连续时间Markov链所确定的多模态It^o随机系统的均方稳定性与鲁棒镇定 ,得到了一般多模态It^o随机系统的k阶矩指数稳定性定理 ,线性不确定系统的均方稳定性定理 ,给出了线性不确定系统的鲁棒镇定控制器 .     

多模态It(o)随机系统的均方稳定性与鲁棒镇定

研究由连续时间Markov链所确定的多模态It?随机系统的均方稳定性与鲁棒镇定,得到了一般多模态It?随机系统的k阶矩指数稳定性定理,线性不确定系统的均方稳定性定理,给出了线性不确定系统的鲁棒镇定控制器.     

多人非合作随机自适应博弈

本文考虑系数未知的离散时间线性随机系统多人非合作的自适应博弈问题,每个参与者运用最小二乘算法和"必然等价原则"来设计博弈策略组合,目的是自适应优化自身的一步超前收益函数.本文证明此自适应策略组合使得闭环系统全局稳定,并且在一定意义下是该博弈问题的渐近纳什均衡解.     

博弈树函数及其计算优化

为了更好地认识博弈树搜索算法的导出背景,我们抽象提取了博弈问题求解的特征,发展了刻划问题的表达函数及其计算优化的一组定义和定理,以用于分析综合博弈问题的求解策略.它们帮助我们推导出了α-β,CSS料和S等新算法和改良算法. 我们在本文中介绍了这些定义,给出了定理的证明,并且列表显示了这些结果对导出博弈树搜索算法的影响和对算法性能的影响.     

多智能体系统中基于演化博弈的群体状态控制

在对多智能体系统的研究中,如何通过施加最少的控制来使某种策略在群体中占优是一个未解的难题.本文借助演化博弈理论,通过设置一定比例节点为指定策略作为控制手段,分别研究了在无结构群体和随机规则网络群体中的策略演化情况.在随机规则网络中,本文进一步研究了在控制手段下,一种新策略是如何演化并成功占据整个网络的.结果表明在无结构的情况下,强制策略对群体的影响受限于博弈的类型;而在随机规则网络中,在任何的博弈类型下,只要给定足够多的强制策略就可以使其突破成功.在理论分析的基础上,本文进行了计算机仿真验证,仿真结果与理论结果一致.本文的结果揭示了如何对群体施加影响,进而对群体中的个体状态进行控制.     

随机时滞系统的滤波稳定性与渐近性

本文对于用二阶向量差分方程描述的随机时滞系统,用增广差分方程的方法给出了数字滤波的稳定性定理和滤波误差方差阵的渐近性定理。释例计算表明,其结果与理论分析是一致的。     

一类离散时间非齐次马尔可夫跳跃系统最优控制

本文研究了一类离散时间非齐次马尔可夫跳跃线性系统的线型二次高斯(linear quadratic Gaussian,LQG)问题,其中系统模态转移概率矩阵随时间随机变化,其变化特性由一高阶马尔可夫链描述.对于该系统的LQG问题,文中首先给出了线性最优滤波器,得到最优状态估计;其次,验证分离定理成立,并利用利用动态规划方法设计了系统最优控制器;最后,数值仿真结果验证了所设计控制器的有效性.     

二维平面网格上移动成本群体合作行为研究

从移动成本、收益期望与空间博弈的角度,探讨多主体系统的博弈策略演化与系统涌现特征之间的关系。利用空间演化博弈理论,构建了基于个体移动机制的拓扑结构时刻演变的空间演化博弈模型,分析了当主体具有不同的移动成本与收益期望时系统演化的稳定策略,通过分析稳定策略深入探讨系统中合作簇涌现的机理。仿真结果表明,提高移动成本能够最有效地促进系统合作率,同时中等水平的个体收益期望会进一步促进高移动成本的影响效果。     

Zakai equation of nonlinear filtering with unbounded coefficients. The case of dependent noises

In this paper, we prove that the unnormalized filter associated with nonlinear filtering problems with dependent noises and a one-dimensional observations process the coefficients of which are unbounded solves a parabolic stochastic partial differential equation, the Zakai equation. The robust form of the Zakai equation is also computed.     

Necessary and sufficient conditions of risk‐sensitive optimal control and differential games for stochastic differential delayed equations

In this paper, we consider risk‐sensitive optimal control and differential games for stochastic differential delayed equations driven by Brownian motion. The problems are related to robust stochastic optimization with delay due to the inherent feature of the risk‐sensitive objective functional. For both problems, by using the logarithmic transformation of the associated risk‐neutral problem, the necessary and sufficient conditions for the risk‐sensitive maximum principle are obtained. We show that these conditions are characterized in terms of the variational inequality and the coupled anticipated backward stochastic differential equations (ABSDEs). The coupled ABSDEs consist of the first‐order adjoint equation and an additional scalar ABSDE, where the latter is induced due to the nonsmooth nonlinear transformation of the adjoint process of the associated risk‐neutral problem. For applications, we consider the risk‐sensitive linear‐quadratic control and game problems with delay, and the optimal consumption and production game, for which we obtain explicit optimal solutions.     

Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise

We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the type of convergence we consider is almost sure uniform convergence, i.e. pathwise convergence. The proofs are based on a recent perturbation result for such equations.     

A varying terminal time structure for stochastic optimal control under constrained condition

In this study, we propose a varying terminal time structure for the optimal control problem under state constraints, in which the terminal time follows the varying of the control via the constrained condition. Focusing on this new optimal control problem, we investigate a novel stochastic maximum principle, which differs from the traditional optimal control problem under state constraints. The optimal pair of the optimal control model can be verified via this new stochastic maximum principle.     

The Kalman-Bucy Filter for Linear Stochastic Dynamic Systems with Discontinuous Trajectories

An optimal linear filtration problem is considered in the paper based on Kalman-Bucy results. The sequential linear regression method being a modification of fundamental Wiener results is used.     

Explicit solutions of a class of linear fractional BSDEs

We obtain explicit solutions for a class of linear backward stochastic differential equations driven by a fractional Brownian motion with arbitrary Hurst parameter via the solution of a partial differential equation and a fractional Itô formula.     

基于鲁棒控制的期权套期保值策略

在标的资产价格服从带有随机方差几何布朗运动的非完全市场假设条件下,应用随机微分对策方法,研究与标的资产有关的欧式期权的动态套期保值策略问题。建立了最优动态套期保值策略的随机微分对策数学模型,给出了基于鲁棒控制的均方复制误差最小的自融资动态套期保值策略。当方差为时间的确定性函数时,最优动态套期保值策略与用Black-Scholes套期比表示的delta套期保值策略是一致的。     

Non‐Zero Sum Differential Games of Backward Stochastic Differential Delay Equations Under Partial Information

In this paper, we study a new type of differential game problems of backward stochastic differential delay equations under partial information. A class of time‐advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. By means of ASDEs, we suggest the necessary and sufficient conditions called maximum principle for an equilibrium point of non‐zero sum games. As an application, an economic problem is putted into our framework to illustrate the theoretical results. In terms of the maximum principle and some auxiliary filtering results, an equilibrium point is obtained.     

Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs

In this paper we present a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a conditional probability density function (PDF) in each element and subsequently implement generalized Polynomial Chaos (gPC) locally. Numerical examples show that ME-gPC exhibits both p- and h-convergence for arbitrary probability measures