In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating acco...In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.展开更多
Erlang风险模型广泛应用于排队论、控制论以及金融风险过程。本文在索赔来到(claim-arrival)为Erlang过程,索赔额服从帕雷托分布以及具有常数利息力度的假设下,得到了有限时间内破产概率的渐近表达公式。该结果实质性地推广了Kluppelber...Erlang风险模型广泛应用于排队论、控制论以及金融风险过程。本文在索赔来到(claim-arrival)为Erlang过程,索赔额服从帕雷托分布以及具有常数利息力度的假设下,得到了有限时间内破产概率的渐近表达公式。该结果实质性地推广了Kluppelberg and Stadtmuller[1]和Tang[2]的结果:前者考虑了无穷时间的破产概率,而后者考虑的过程局限为泊松的。由破产模型与排队模型之间的联系可知,本文的结果在管理科学中有许多应用。展开更多
基金supported by the National Natural Science Foundation of China(11101451)Ph.D.Programs Foundation of Ministry of Education of China(20110191110033)
文摘In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.
文摘Erlang风险模型广泛应用于排队论、控制论以及金融风险过程。本文在索赔来到(claim-arrival)为Erlang过程,索赔额服从帕雷托分布以及具有常数利息力度的假设下,得到了有限时间内破产概率的渐近表达公式。该结果实质性地推广了Kluppelberg and Stadtmuller[1]和Tang[2]的结果:前者考虑了无穷时间的破产概率,而后者考虑的过程局限为泊松的。由破产模型与排队模型之间的联系可知,本文的结果在管理科学中有许多应用。
