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Journal of Systems Science & Complexity 2011年第1期24卷 156-166页

作者： Ming ZHOU Hongbin DONG Jingfeng XU China Institute for Actuarial Sciences Central University of Finance and Economics Beijing 100081 China

This paper considers the problem of minimizing the VaR and CTE of an insurer＇s retained risk by controlling the combinational quota-share and stop-loss reinsurance strategy. With a constrained reinsurance premium, the authors give the explicit reinsurance forms and the minimal VaR and CTE of retained risk in the case of quota-share after stop-loss reinsurance and the case of stop-loss afterquota-share reinsurance respectively. Finally, the authors conclude that the quota-share after stop-loss is a better reinsurance strategy than stop-loss after quota-share to minimize the VaR and CTE with a same constrained reinsurance premium. And the pure stop-loss reinsurance is preferred for an insurer with a high level regulatory requirement.

关键词： Conditioned Tailed Expectation (CTE) after quota-share Value at Risk (VaR). quota-share after stop-loss reinsurance stop-loss

Optimal Time-consistent Investment and reinsurance Strategy for Mean-variance Insurers Under the Inside Information

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 1087-1100页

作者： Jing CAO Xing-chun PENG Yi-jun HU School of Mathematics and Statistics Wuhan University School of Mathematics and Statistics South-Central University for Nationalities School of Science Wuhan University of Technology

In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.

关键词： reinsurance portfolio inside information time-consistency mean-variance criterion

On Optimal Proportional reinsurance and Investment in a Markovian Regime-Switching Economy

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Acta Mathematica Sinica,English Series 2012年第1期28卷 67-82页

作者： Xin ZHANG Tak Kuen SIU School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071P.R.China Department of Actuarial Studies Faculty of Business and EconomicsMacquarie UniversitySydneyNSW 2109Australia

In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.

关键词： reinsurance regime-switching economy optimal investment short-selling constraints

Optimal proportional reinsurance and investment problem with jump-diffusion risk process under effect of inside information

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Frontiers of Mathematics in China 2014年第4期9卷 965-982页

作者： Jie XIONG Shuaiqi ZHANG Hui ZHAO Xihuan ZENG Department of Mathematics FST University of Macao Macao China School of Economics and Commerce Guangclong University of TechnologyGuangzhou 510520 China Department of Statistics Hebei University of Technology Tianjin 300401 China Department of Mathematics Tianjin University Tianjin 300072 China Institute of Business Administration University of Macao Macao China

We study optimal investment and proportional reinsurance strategy in the presence of inside information. The risk process is assumed to follow a compound Poisson process perturbed by a standard Brownian motion. The insurer is allowed to invest in a risk-free asset and a risky asset as well as to purchase proportional reinsurance. In addition, it has some extra information available from the beginning of the trading interval, thus introducing in this way inside information aspects to our model. We consider two optimization problems： the problem of maximizing the expected exponential utility of terminal wealth with and without inside information, respectively. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Finally, we discuss the effects of parameters on the optimal strategy and the effect of the inside information by numerical simulations.

关键词： Inside information investment reinsurance jump diffusion

Risk-based Optimal Investment and Proportional reinsurance of an Insurer with Hidden Regime Switching

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 755-770页

作者： Xing-chun PENG Yi-jun HU School of Science Wuhan University of Technology School of Mathematics and Statistics Wuhan University

In this paper, we study the optimal investment and proportional reinsurance strategy for an insurer in a hidden Markov regime-switching environment. A risk-based approach is considered, where the insurer aims at selecting an optimal strategy with a view to minimizing the risk described by a convex risk measure of its terminal wealth. We solve the problem in two steps. First, we employ the filtering theory to turn the optimization problem with partial observations into one with complete observations. Second, by using BSDEs with jumps, we solve the problem with complete observations.

关键词： investment reinsurance hidden Markov chain convex risk measure backward stochastic differential equation

OPTIMAL PROPORTIONAL reinsurance AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

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Acta Mathematica Scientia 2015年第2期35卷 303-312页

作者：周杰明邓迎春黄娅杨向群 School of Mathematical Sciences Nankai University College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal University College of Business Administration Hunan University

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

关键词： Constant elasticity of variance Hami!ton-Jacobi-Bellman equation jump-diffusion process exponential utility reinsurance

Dividend-reinsurance Strategy in the Sparre Andersen Model

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Acta Mathematica Sinica,English Series 2013年第2期29卷 405-416页

作者： Ji Yang TAN Lin XIAO Shao Yue LIU Xiang Qun YANG Department of Statistics Xiangtan University HPCSIP Key Laboratory Ministry of Education Department of Mathematics Hu'nan Normal University

In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.

关键词： Sparre Andersen model reinsurance expected discounted penalty function iteration constant dividend barrier

THE OPTIMAL reinsurance-INVESTMENT PROBLEM CONSIDERING THE JOINT INTERESTS OF AN INSURER AND A REINSURER UNDER HARA UTILITY

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Acta Mathematica Scientia 2023年第1期43卷 97-124页

作者：张燕赵培标周华任 Department of General Education Army Engineering University of PLANanjing211101China School of Mathematics&Statistics Nanjing University of Science and TechnologyNanjing210094China

This paper focuses on an optimal reinsurance and investment problem for an insurance corporation which holds the shares of an insurer and a *** that the insurer can purchase reinsurance from the reinsurer,and that both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset which are governed by the Heston model and are distinct from one *** aim to find the optimal reinsuranceinvestment strategy by maximizing the expected Hyperbolic Absolute Risk Aversion(HARA)utility of the insurance corporation’s terminal wealth,which is the weighted sum of the insurer’s and the reinsurer’s terminal *** Hamilton-Jacobi-Bellman(HJB)equation is first ***,this equation is non-linear and is difficult to solve directly by any ordinary method found in the existing literature,because the structure of this HJB equation is more complex under HARA *** the present paper,the Legendre transform is applied to change this HJB equation into a linear dual one such that the explicit expressions of optimal investment-reinsurance strategies for-1≤ρi≤1 are *** also discuss some special cases in a little bit more ***,numerical analyses are provided.

关键词： reinsurance investment HARA utility Heston model Legendre transform

Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection

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Science China Mathematics 2010年第7期53卷 1784-1801页

作者： Bai LiHua Guo JunYi Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China

In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson's longstanding conjecture about the relation between the two problems.

关键词： exponential utility Hamilton-Jacobi-Bellman equation multiple risky asset investment proba- bility of ruin excess-of-loss reinsurance

OPTIMAL reinsurance UNDER EXPECTED VALUE PRINCIPLE

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Applied Mathematics(A Journal of Chinese Universities) 2006年第4期21卷 454-460页

作者： Cao Yusong Zhang Yi College of Computer Science ＆ Technology Xuchang University Xuchang 461000 China. Department of Mathematics Zhejiang University Hangzhou 310028 China.

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.

关键词： reinsurance expected value principle variance risk measure Lagrangian function.