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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

The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by Ito-Lévy Processes

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Journal of Systems Science & Complexity 2019年第4期32卷 997-1018页

作者： WANG Wencan WU Jinbiao liu zaiming School of Control Science and Engineering Shandong UniversityJinan 250061China School of Mathematics and Statistics Central South UniversityChangsha 410083China

This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial *** existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all *** proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.

关键词： Forward-backward doubly stochastic differential equations Ito-Lévy processes linear quadratic problem maximum principle variational equation

Markov branching processes with immigration-migration and resurrection

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Science China Mathematics 2011年第5期54卷 1043-1062页

作者： LI JunPing liu zaiming School of Mathematical Science and Computing Technology Central South University Changsha 410075 China

We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.

关键词： Markov branching process, immigration, migration, resurrection, regularity, extinction, recurrence, ergodicity收藏本站首页期刊全文库学位论文库会议论文库吾喜杂志注册|登录|我的账户基础科学|工程科技I辑|工程科技II辑|医药卫生科技|信息科技|农业科技|哲学与人文科学|社会科学I辑|社会科学II辑|经济管理高级搜索: 用" Markov branching process immigration "到知网平台检索,点击这里搜索更多...《Science China(Mathematics)》 2011年05期加入收藏获取最新 Markov branching processes with immigration-migration and resurrection【摘要】: We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.【关键词】 : Markov branching process immigration migration resurrection regularity extinction recur- rence ergodicity Keywords Markov branching process, immigration, migration, resurrection, regularity, extinction, recur-rence, ergodicity

The application of the entropy-based statistic for genomic association study of QTL

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Journal of Genetics and Genomics 2008年第3期35卷 183-188页

作者： Yang Xiang Yumei Li zaiming liu Zhenqiu Sun College of Mathematics Central South University Changsha 410081 China School of Public Health Central South University Changsha 410078 China Mathematics Department of Huaihua College Huaihua 418000 China

An entropy-based statistic TpE has been proposed for genomic association study for disease-susceptibility locus. The statistic TpE may be directly adopted and/or extended to quantitative-trait locus （QTL）mapping for quantitative traits. In this article, the statistic TpE was extended and applied to quantitative trait for association analysis of QTL by means of selective genotyping. The statistical properties （the type I error rate and the power） were examined under a range of parameters and population-sampling strategies （e.g., various genetic models, various heritabilities, and various sample-selection threshold values） by simulation studies. The results indicated that the statistic TpE is robust and powerful for genomic association study of QTL. A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms （SNPs） of angiotensin-I converting enzyme genes was conducted to evaluate the performance of the statistic TPE for genetic association study.

关键词： entropy quantitative-trait locus association analysis extreme sample

Markov skeleton processes

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Chinese Science Bulletin 1998年第11期43卷 881-889页

作者： Hou Zhenting liu zaiming Zou Jiezhong Changsha Railway Univ Res Dept Changsha 410075 Peoples R China

A new class of stochastic processes--Markov skeleton processes is introduced, which have the Markov property on a series of random times. Markov skeleton processes include minimal Q processes, Doob processes, Q processes of order one, semi-Markov processes , piecewise determinate Markov processes , and the input processes, the queuing lengths and the waiting times of the system GI/G/1, as particular cases. First, the forward and backward equations are given, which are the criteria for the regularity and the formulas to compute the multidimensional distributions of the Markov skeleton processes. Then, three important cases of the Markov skeleton processes are studied: the (H, G, Π)-processes, piecewise determinate Markov skeleton processes and Markov skeleton processes of Markov type. Finally, a vast vistas for the application of the Markov skeleton processes is presented.

关键词： Markov skeleton Markov skeleton process (H Q)-process the normal Morkov skeleton process.

ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

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Acta Mathematica Scientia 2019年第5期39卷 1345-1362页

作者： Yuejiao WANG zaiming liu Quansheng liu Yingqiu LI College of Mathematics and Computational Science Hunan First Normal University Changsha 410205 China School of Mathematics and Statistics Central South University Changsha 410083 China LMBA UMR CNRS 6205 Université de Bretagne-Sud F-56000 Vannes France School of Mathematics and Statistics Changsha University of Science and Technology Changsha 410004 China

We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.

关键词： branching random walk random environment quenched moments weighted moments

Optimal Admission and Price Control in a Retrial Queueing System 36

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Optimal Admission and Price Control in a Retrial Queueing Sy...

Clinical Value of Interventional Embolization for Sacral Chordoma before Surgical Treatment

第36届中国控制会议

作者： zaiming liu Wei Deng Gang Chen School of Mathematics and Statistics Central South University

ISBN: (纸本)9781538629185

In this paper, we analyze the optimal control policy to minimize the average costs in a retrial queueing system. At any decision epoch, the manager uses admission probabilities a’s to control the arriving customers and determines a cancellation price c for the unsuccessful retrial customer, which will lead to him out of system with the probability of G（c） otherwise back to the orbit. We cast the problem as a Markov decision process and derive that the optimal policy has a pure threshold form. We also show that the two thresholds are monotonic in system parameters. Furthermore, based on the structure of the optimal policy,we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by solving the quasi-birth-death（QBD） process. Finally, some numerical experiments are presented to illustrate the effect of the system parameters on the optimal policy.

关键词： Retrial queueing system Markov decision process Matrix analytic method Performance evaluation

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放射学实践 2011年第6期26卷 649-652页

作者： Zhihui CHANG Zhaoyu liu Jiahe Zheng zaiming LU Qiyong GUO Department of Radiology Shengjing Hospital of China Medical University Shenyang 110004 China

Objetive:To evaluate the efficacy of preoperative transcatheter arterial embolization in the treatment of sacral chordoma,and to explore the choice of embolization ***:32 patients underwent the posterior approach after TAE of the main arteries that supplied the sacral *** bleeding amount of each patient was recorded and compared between-group differences at different operation ***:After embolization,12 patients were received resection within 24 hours(group A),that of 10 cases between 24~48h(group B),of another 10 cases between 48~72h(group C).All of the 32 tumors were removed intact with intraoperative bleeding about(894±199)ml,without any shock or death,nor injuries on abdominal organs such as rectum and *** was no statistical significance in tumor size among group A,B and C(P>0.05).Data gave statistical significance in intraoperative blood loss between group A and B(P0.05),in spite of group B slightly less than group ***:Preoperative TAE for excising the sacral tumor can significantly decrease intraoperative blood loss,make the surgical field clear,and facilitate the maximal removal of the sacral *** would be best to select the embolization timing within 24 hours before surgical operation.

关键词：摘要编辑部编辑工作读者

基于Pareto最优风险转换的联合共保模型及其破产概率

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应用数学学报 2011年第4期34卷 618-633页

作者：肖晴初湖南商学院信息学院长沙410205 中南大学数学科学与计算技术学院长沙410075

本文从联合保险市场Pareto最优风险转换出发,考虑保险公司不仅是分出再保险自己公司承保的风险,也可以分入再保险以分保其他公司的风险,整个保险市场的各公司之间是相互承保的,形成一个联合共保的市场整体,依据Borch的市场均衡理论,建... 详细信息

本文从联合保险市场Pareto最优风险转换出发,考虑保险公司不仅是分出再保险自己公司承保的风险,也可以分入再保险以分保其他公司的风险,整个保险市场的各公司之间是相互承保的,形成一个联合共保的市场整体,依据Borch的市场均衡理论,建立了保险公司之间联合比例分保模型,同时给出了风险转移矩阵的基本性质、各保险公司的安全荷载系数、各公司之间相关度以及各保险公司的破产概率,最后给出了有关联合共保及Pareto最优风险转换的实例分析.

关键词：再保险联合共保 Pareto最优 Borch均衡比例再保险破产概率