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On the expected discounted penalty function for a Risk Process with Stochastic Return on Investments

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Journal of Mathematical Research and Exposition 2010年第2期30卷 309-318页

作者： Li Li LI Jing Hal FENG Li Xin SONG School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China

This paper considers the expected discounted penalty function Φ（u） for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ （0） is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.

关键词： expected discounted penalty function integro-differential equation Laplace transform ruin.

A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 625-632页

作者： Hu Yang Yuan-yuan Hao College of Mathematics and Statistics Chongqing UniversityChongqing400030China

In this paper,we consider a generalization of the classical ruin model,where the income is random and the distribution of the time between two claim occurrences depends on the previous claim *** model is more appropriate than the classical ruin *** expression for the generating function of the Gerber-Shiu expected discounted penalty function are derived.A similar model is ***,the result are showed by two examples.

关键词： Ruin model expected discounted penalty function dependence ruin probability

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