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The Stochastic Maximum Principle for a Jump-Diffusion Mean-Field Model Involving Impulse Controls and Applications in Finance

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Journal of Systems Science & Complexity 2020年第1期33卷 26-42页

作者： LI Cailing LIU Zaiming wu jinbiao HUANG Xiang School of Mathematics and Statistics Central South UniversityChangsha 410083China Research and Development Center Agricultural Bank of ChinaBeijing 100161China

This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse *** authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse *** for its application,a mean-variance portfolio selection problem has been solved.

关键词： Impulse control jump-diffusion Markowitz’s mean-variance model stochastic maximum principle

CONVERGENCE ANALYSIS ON ITERATIVE METHODS FOR SEMIDEFINITE SYSTEMS

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Journal of Computational Mathematics 2008年第6期26卷 797-815页

作者： jinbiao wu Young-Ju Lee Jinchao Xu Ludmil Zikatanov LMAM and School of Mathematical Sciences Peking University Beijing 100871 China Department of Mathematics Rutgers The State University of New Jersey Busch Campus Piscataway NJ 08854-8019 USA Department of Mathematics The Pennsylvania State University University Park PA16802 USA Department of Mathematics The Pennsylvania State University University Park PA 16802 USA

The convergence analysis on the general iterative methods for the symmetric and positive semidefinite problems is presented in this paper. First, formulated are refined necessary and sumcient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate identity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The uniform convergence of multigrid method for a model problem is proved by the convergence rate identity. The work can be regradled as unified and simplified analysis on the convergence of iteration methods for semidefinite problems [8, 9].

关键词： Semidefinite systems Subspace correction methods Iterative methods Energy norm convergence.

Optimal Control of Fully Coupled Forward-Backward Stochastic Systems with Delay and Noisy Memory 36

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Optimal Control of Fully Coupled Forward-Backward Stochastic...

A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach

第36届中国控制会议

作者： jinbiao wu Wencan Wang Yi Peng School of Mathematics and Statistics Central South University Junior Education Department Changsha Normal University

ISBN: (纸本)9781538629185

We study the optimal control of fully coupled forward-backward stochastic systems with delay and noisy memory where the dynamics is governed by a controlled It?-Lévy process and the information available to the controller is possibly less than the overall information. Sufficient and necessary maximum principles for the optimal control of such systems are derived using Malliavin calculus techniques. As an illustration, we apply the result to an optimal consumption problem in a financial model with memory and partial information.

关键词： Stochastic Optimal Control Forward-Backward Stochastic Systems Stochastic Maximum Principle Noisy Memory Malliavin Calculus

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Communications in Computational Physics 2012年第7期12卷 544-576页

作者： Satoshi Ii Xiaobo Gong Kazuyasu Sugiyama jinbiao wu Huaxiong Huang Shu Takagi Department of Mechanical Engineering The University of Tokyo7-3-1 Hongo Bunkyo-kuTokyo113-8656Japan Department of Engineering Mechanics NAOCEShanghai Jiaotong UniversityShanghai 200240China LMAM&School of Mathematical Sciences Peking UniversityBeijing 100871China Department of Mathematics and Statistics York University4700 Keele StreetTorontoOntarioCanada Computational Science Research Program RIKEN2-1 Hirosawa WakoSaitama351-0198Japan.

A novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh is proposed within the framework of the volume-of-fluid *** present method is based on a full Eulerian fluid-(bulk)structure coupling solver(Sugiyama et al.,***.,230(2011)596–627),with the bulk structure replaced by elastic *** this study,a closed membrane is considered,and it is described by a volume-of-fluid or volume-fraction information generally called VOF function.A smoothed indicator(or characteristic)function is introduced as a phase indicator which results in a smoothed VOF *** smoothed VOF function uses a smoothed delta function,and it enables a membrane singular force to be incorporated into a mixture momentum *** order to deal with a membrane deformation on the Eulerian mesh,a deformation tensor is introduced and updated within a compactly supported region near the *** the neo-Hookean and the Skalak models are employed in the numerical simulations.A smoothed(and less dissipative)interface capturing method is employed for the advection of the VOF function and the quantities defined on the *** stability restriction due to membrane stiffness is relaxed by using a quasi-implicit *** present method is validated by using the spherical membrane deformation problems,and is applied to a pressure-driven flow with the biconcave membrane capsules(red blood cells).

关键词： Fluid-membrane interaction Eulerian formulation Cartesian mesh volume-of-fluid quasi-implicit approach red blood cell

Optimal control for a zero-sum stochastic differential game with noisy memory under g-expectation

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Optimal control for a zero-sum stochastic differential game ...

第37届中国控制会议

作者： jinbiao wu Hongchao Qian School of Mathematics and Statistics Central South University

We study the optimal control for a zero-sum stochastic differential game with noisy memory under g-expectation where the dynamics is governed by a controlled It?-Lévy process and the information available to the controller is possibly less than the overall information. Sufficient and necessary maximum principles for the optimal control of such systems are derived using Malliavin calculus techniques. As an illustration, we apply the result to a stochastic differential portfolio game problem in a financial model with memory and partial information.

关键词： Stochastic Optimal Control Stochastic Differential Game Stochastic Maximum Principle Noisy Memory gexpectations

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椭圆型方程内边界问题的数值逼近(英文)

北京大学学报（自然科学版） 2000年第1期36卷 20-28页

作者：吴金彪北京大学数学科学学院北京100871

讨论了椭圆型偏微分方程内边界问题的数值逼近。对变系数内边界问题，介绍了一种特殊的有限元方法。该方法结合了无限元方法，使在奇点附近的奇性解得到好的逼近。证明了该方法具有与有限元方法对正则解相同的精确度。最后给出了计算的... 详细信息

讨论了椭圆型偏微分方程内边界问题的数值逼近。对变系数内边界问题，介绍了一种特殊的有限元方法。该方法结合了无限元方法，使在奇点附近的奇性解得到好的逼近。证明了该方法具有与有限元方法对正则解相同的精确度。最后给出了计算的实例。

关键词：椭圆型方程内边界问题数值逼近

Singular optimal control of a generalized backward doubly stochastic system with general jumps

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Singular optimal control of a generalized backward doubly st...

第三十九届中国控制会议

作者： Yi Peng jinbiao wu Rongren Zhu School of Mathematical Sciences Changsha Normal University School of Mathematics and Statistics Central South University

In this paper, we study the singular optimal control problem of a generalized backward doubly stochastic system with general jumps. By the method of convex variation and duality technique, we establish sufficient and necessary maximum principles for the optimal control of such stochastic system. This result is a generalization of the maximum principles to singular optimal control problems for backward stochastic systems.

关键词： Generalized backward doubly stochastic differential equation Singular stochastic optimal control Stochastic maximum principle Lévy process

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D-N交替迭代法及其收敛性分析

数值计算与计算机应用 2002年第2期23卷 121-130页

作者：吴金彪北京大学数学科学学院

§1.D-N交替法介绍区域分解算法是八十年代以来发展的一个较新的算法.该方法是应大规模科学和工程计算的需要而产生的.它的基本想法相当简单,但由于该算法具有一系列优点,如能将大型问题的求解分解成小型问题的求解,将复杂边值问题的求... 详细信息

§1.D-N交替法介绍区域分解算法是八十年代以来发展的一个较新的算法.该方法是应大规模科学和工程计算的需要而产生的.它的基本想法相当简单,但由于该算法具有一系列优点,如能将大型问题的求解分解成小型问题的求解,将复杂边值问题的求解转化成简单边值问题的求解,将串行问题转化成并行问题的求解等.所以它是计算数学的热门问题之一.

关键词： D-N交替迭代法收敛性分析区域分解算法弹性力学偏微分方程

具有N策略和负顾客的反馈抢占型的M/G/1重试可修排队系统

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应用数学学报 2009年第2期32卷 323-335页

作者：吴锦标尹小玲刘再明中南大学概率统计研究所长沙410075 中山大学数学与计算科学学院广州510275

本文研究了具有N策略和负顾客的反馈抢占型的M/G/1重试可修排队系统.所有顾客(包括正顾客和负顾客)的到达都是泊松过程,服务器是可修的.利用吸收分布,求出了系统存在稳态的充分必要条件.利用补充变量法,求出了系统稳态时系统和重试区域... 详细信息

本文研究了具有N策略和负顾客的反馈抢占型的M/G/1重试可修排队系统.所有顾客(包括正顾客和负顾客)的到达都是泊松过程,服务器是可修的.利用吸收分布,求出了系统存在稳态的充分必要条件.利用补充变量法,求出了系统稳态时系统和重试区域中队长分布的概率母函数,以及其他一些重要的排队指标.

关键词： N策略负顾客反馈抢占重试