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EXPECTED DISCOUNTED PENALTY FUNCTION OF ERLANG(2) RISK MODEL WITH CONSTANT INTEREST 被引量:3
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作者 Nie Gaoqin Liu Cihua Xu Lixia 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第3期243-251,共9页
The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang(2) risk process under constant interest force. An integro-differential equation satisfied by the expected... The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang(2) risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case. 展开更多
关键词 expected discounted penalty function Erlang(2) process Laplace transform interest rate integro-differential equation defective renewal equation.
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On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments 被引量:1
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作者 Li Li LI Jing Hal FENG Li Xin SONG 《Journal of Mathematical Research and Exposition》 CSCD 2010年第2期309-318,共10页
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 exp... 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. 展开更多
关键词 expected discounted penalty function integro-differential equation Laplace transform ruin.
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The Gerber-Shiu Expected Discounted Penalty Function for Lévy Insurance Risk Processes
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作者 Xiang-hua Zhao Chuan-cun Yin 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第4期575-586,共12页
In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk mode... In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity. 展开更多
关键词 Lévy process Gerber-Shiu expected discounted penalty function renewal equation time of ruin
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A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals 被引量:2
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作者 Hu Yang Yuan-yuan Hao 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第4期625-632,共8页
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 size.This model is more ap... 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 size.This model is more appropriate than the classical ruin model.Explicit expression for the generating function of the Gerber-Shiu expected discounted penalty function are derived.A similar model is discussed.Finally,the result are showed by two examples. 展开更多
关键词 Ruin model expected discounted penalty function DEPENDENCE ruin probability
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Dividend-Reinsurance Strategy in the Sparre Andersen Model
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作者 Ji Yang TAN Lin XIAO +1 位作者 Shao Yue LIU Xiang Qun YANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第2期405-416,共12页
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 stra... 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. 展开更多
关键词 Sparre Andersen model REINSURANCE expected discounted penalty function ITERATION constant dividend barrier
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