The maximum principle for partially observed optimal control of forward-backward stochastic systems with random jumps

This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.     

Maximum principle for forward-backward stochastic control system with random jumps and applications to finance

<正> Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.     

Backward linear-quadratic stochastic optimal control and nonzero-sum differential game problem with random jumps

This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps. The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations. The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed. All these results develop those of Lim, Zhou (2001) and Yu, Ji (2008).     

Controlled mean-field backward stochastic differential equations with jumps involving the value function

This paper discusses mean-field backward stochastic differential equations (mean-field BSDEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.     

随机线性二次最优控制在投资组合中的应用

提出一类随机线性二次最优控制问题,给出了一个新的随机黎卡提方程,若此方程有解,就可以得到系统的最优反馈控制;作为其应用,讨论了连续时间的均值-方差投资组合选择问题,其目标是投资组合的最终收益最大,风险最小,通过"嵌入"方法将其转化为随机线性二次最优控制问题,并在非自融资的条件下,得出最优证券组合;最后将其理论应用于实例分析.     

带跳市场中随机利率下的美式—亚式期权定价

在假设期权标的资产价格服从跳跃-扩散模型、利率遵循短期随机利率模型的基础上,运用总体最小二乘拟蒙特卡罗方法为美式-亚式期权定价,并将得到的定价结果和不带跳市场中美式-亚式期权的价格进行比较,数值结果表明,运用总体最小二乘拟蒙特卡罗方法得到的期权价格更好地反映了实际期权价格,并且该方法用于美式-亚式期权定价是合理的,时效性强,收敛速度快.     

一类单一物品随机库存系统的最优控制模型

研究单一物品随机库存系统的最优控制问题，并借助于动态规划原理给出了了优控制律的表达式，以使在一个时间周期[0,T]内系统的费用总和的期望值最小。     

Pricing credit derivatives under fractional stochastic interest rate models with jumps

Based on the reduced-form approach, this paper investigates the pricing problems of default-risk bonds and credit default swaps (CDSs) for a fractional stochastic interest rate model with jump under the framework of primary-secondary. Using properties of the quasi-martingale with respect to the fractional Brownian motion and the jump technique in Park (2008), the authors first derive the explicit pricing formula of defaultable bonds. Then, based on the newly obtained pricing formula of defaultable bonds, the CDS is priced by the arbitrage-free principle. This paper presents an extension of the primary-secondary framework in Jarrow and Yu (2001).     

Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls

This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls, which have potential applications in mathematical finance.     

On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

<正> This paper presents the notions of exact observability and exact detectability for Markovjump linear stochastic systems of Ito type with multiplicative noise (for short,MJLSS).StochasticPopov-Belevith-Hautus (PBH) Criterions for exact observability and exact detectability are respectivelyobtained.As an application,stochastic H_2/H_∞ control for such MJLSS is discussed under exactdetectability.     

含污染控制的多车型随机交通系统最优收费及其评价

针对车辆特征的差异, 将用户按车型分为有限类,用户依据出行成本随机选择出行路径.为了达到合理分配流量和减少排污的目的,交通管理者按车型对用户收取拥挤税和污染税.通过建立多车型随机变分不等式模型,得到了包含拥挤税和污染税的依车型的最优收费,最后提出了基于效率损失的政策评价指标. 数值试验表明:随着环保强度加大, 系统总污染逐渐下降, 评价指标有效.     

Maximum principle for partially-observed optimal control problems of stochastic delay systems

This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov’s theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.     

随机系统待机控制特征量指标约束下的满意PID控制

研究一类随机系统同时具有期望的待机特征量指标和衰减度指标约束的满意PID控制问题.首先基于边界穿越定理,给出一种确定使闭环系统稳定和使闭环系统满足期望的衰减度指标约束的PID控制器参数解集的方法.再基于待机控制理论,推导出满足期望的待机特征量指标:平均滞留时间和平均待机时间指标约束的PID控制器参数解集表达式.应用满意控制思想,对上述期望指标的相容性进行了分析,给出了确定相容指标取值范围的有效算法,以及当期望指标相容时PID控制器参数解集的求取策略.用一个算例说明了该方法的可行性和有效性.     

An optimal stochastic approximation for estimating the effective window of a control factor

For control processes with one control factor and ternary response, it is important to ?nd the effective settings of the control factor. Especially, it is often of scienti?c and practical interest to?nd the window of the control factor that is necessary to cause the probability of normal response larger than a speci?ed p. This article proposes an optimal stochastic approximation to estimate the window of interest. Simulation study shows that the proposed method gives an effcient estimation with small sample size.     

信息不确定下的主动打断项目组合选择问题鲁棒优化

在项目组合选择问题中,历史数据的缺乏以及预测和估计过程中出现的不可避免的误差,会导致模型中的参数无法被准确地估计,进而给决策带来巨大的风险.因此,构建合适的鲁棒优化模型,为企业提供能有效应对参数不确定性的鲁棒解,对企业的风险防范具有极其重要的现实意义.本文首先对确定参数下的主动打断项目组合选择问题数学模型的特点进行了分析.进一步地,介绍了鲁棒优化问题中不确定情境集的概念,并给出了允许管理者根据其偏好确定不确定情境集大小的方法,构建了全新的基于情境的鲁棒优化模型,进而计算出在所规定的不确定情境集内的最坏情境下能保持可行性与最优性的鲁棒解,实现了鲁棒性与最优性间的权衡,最后,通过GAMS/BARON进行了算例分析,验证了模型的合理性与有效性.从理论上,本文首次将鲁棒优化理论扩展到了主动打断项目组合选择问题中,针对现有的项目组合选择问题鲁棒优化理论仅能应对有限个可行解的不足之处,提出了一类新的鲁棒优化方法,使其能够应对具有无穷多可行解的主动打断项目组合问题.从实践上,随着我国高新产业的发展,具有超前性与特殊性的研究与发展(RD)、信息科技与信息系统(IT/IS)等新兴项目的投资日益受到重视.相较于传统项目,这类项目的高度不确定性使得探究项目组合选择问题的鲁棒优化理论日益迫切.故而本文的研究具有明显的理论价值和现实意义.     

通胀与生存约束下最优投资和自愿退休选择

研究在通胀下,代理人退休选择、最优消费和投资组合决策问题.运用伊藤公式(It?公式)推导了通胀折现的财富动力学方程,基于考虑退休前后的预期消费折现效用最大化标准,利用动态规划方法建立了相应的HJB方程,并求解出最优消费、投资组合与自愿退休选择策略.最后对理论结果给出数值模拟.结果表明,退休前,适当的通胀波动率会带动代理人积极投资,消费反而减少,若通胀波动率过大,代理人会减少投资增加消费来预防通胀风险带来的损失;退休后,代理人的投资和消费均会增加.研究结果对投资者具有参考价值.     

基于不完全信息的商机挖掘的最优停止模型

研究了决策者面对一个重要的商业机会，在掌握不完全信息的情况下，该做出怎样的理性决策才能使企业的期望获利最大或期望损失最小的问题．把商机挖掘看作是一个时间离散、状态连续的马尔柯夫过程，利用信息量与决策不确定性之间的对比关系，建立起动态决策过程的最优停止模型，并给出商机挖掘的最优停止规则．最后给出一个应用案例．     

现代信息技术条件下信息和信息系统再认识

从现代系统理论的观点出发，在全信息理论的基础上重新定义了现代信息技术条件下的信息和信息系统概念．通过对现代信息系统进行分析，将信息系统分解为多个信息跳跃，描述了信息跳跃中的信息创造、表达、传输和吸收过程，为在信息系统分析中引入定量方法打下了基础．     

严格反馈型随机非线性系统输出反馈滑模控制

研究了一类带有不确定性参数的严格反馈型随机非线性系统的输出反馈镇定问题,主要是采用变结构滑模控制方法(SMC)来设计镇定控制器。首先根据系统的结构和输出状态构造了随机非线性状态观测器,并针对结构参数的不确定性,采用梯度自适应调节律,然后基于系统的观测状态选择滑动模切换流形,给出了不含噪声激励的变结构控制律,并证明滑动模的可达性和闭环系统滑模运动的稳定性,最后讨论了滑模控制的抖振抑制问题。通过系统仿真,与其它鲁棒控制方法进行比较,证明了本方法不仅能够有效地镇定该类随机非线性系统,并且具有一些更好的控制性能。     

基于复杂网络理论的指挥控制系统自适应重构模型

为研究信息化条件下指挥控制(command and control, C2)系统在对抗环境下的自适应重构机制,基于复杂网络理论和作战指挥原则,从重构触发机制、边的修复策略、结构重组策略和重构评价机制4方面建立了C2系统的自适应重构模型,其中重点研究了边的修复策略和结构重组策略。针对边的修复提出了一种自适应修复策略;而针对结构重组,提出了升级重组、越级重组、转隶重组和组合重组4种重组策略。仿真结果表明,在综合考虑重构效果和成本消耗的情况下,与以往研究相比,边的自适应修复策略为相对较优的边重构策略,而与单一重组相比,组合重组策略为较优的结构重组策略;并且该自适应重构模型能在一定程度上比较客观地反映指挥控制系统的遇袭重构演化过程。