| 带常利率的Erlang(2)风险模型的罚金折现期望函数 |
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| 引用本文： | 聂高琴,刘次华,徐立霞.带常利率的Erlang(2)风险模型的罚金折现期望函数[J].高校应用数学学报(英文版),2006,21(3):243-251. |
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| 作者姓名： | 聂高琴 刘次华 徐立霞 |
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| 作者单位： | Dept．of Math.,Huazhong Univ．of Science and Technology,Wuhan 430074,Chiina. |
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| 摘 要： | 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.
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| 关 键 词： | 预期值 Laplace变换 利率 缺陷更新方程 积分微分方程 |
| 收稿时间： | 2005-01-19 |
Expected discounted penalty function of erlang(2) risk model with constant interest |
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| Nie Gaoqin,Liu Cihua,Xu Lixia.Expected discounted penalty function of erlang(2) risk model with constant interest[J].Applied Mathematics A Journal of Chinese Universities,2006,21(3):243-251. |
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| Authors: | Nie Gaoqin Liu Cihua Xu Lixia |
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| Institution: | (1) Dept. of Math., Huazhong Univ. of Science and Technology, 430074 Wuhan, China |
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| Abstract: | 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 immediat ely 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. |
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| Keywords: | expected discounted penalty function Erlang(2) process Laplace transform interest rate integro-differential equation defective renewal equation |
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