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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
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In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouche's theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.
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참고문헌 (16)
참고문헌 신청
C. Macci / 2006 / Large deviations for risk models in which each main claim induces a delayed claim / Stochastics 78 (2) : 77 ~ 89
D. C. M. Dickson / 2001 / On the time to ruin for Erlang(2) risk processes / Insur- ance Math. Econom 29 (3) : 333 ~ 344
H. Albrecher / 2004 / A ruin model with dependence between claim sizes and claim intervals / Insurance Math. Econom 35 (2) : 245 ~ 254
H. Albrecher / 2006 / Exponential behavior in the presence of dependence in risk theory / J. Appl. Probab 43 (1) : 257 ~ 273
H. R. Waters / 1985 / Ruin probabilities allowing for delay in claims settlement / IInsurance Math. Econom 4 (2) : 113 ~ 122
D. C. M. Dickson / 2001 / On the time to ruin for Erlang(2) risk processes / Insur- ance Math. Econom 29 (3) : 333 ~ 344
H. Albrecher / 2004 / A ruin model with dependence between claim sizes and claim intervals / Insurance Math. Econom 35 (2) : 245 ~ 254
H. Albrecher / 2006 / Exponential behavior in the presence of dependence in risk theory / J. Appl. Probab 43 (1) : 257 ~ 273
H. R. Waters / 1985 / Ruin probabilities allowing for delay in claims settlement / IInsurance Math. Econom 4 (2) : 113 ~ 122
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