常利率下有阈红利边界的Erlang(2)风险模型的罚金折现期望函数  

The Expected Discounted Penalty Function for the Erlang(2) Risk Model with a Threshold Strategy Under Constant Interest

作　　者：刘向增[1] 田铮[1] 张燕[2] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]中国人民解放军理工大学数学系,南京211101

出　　处：《工程数学学报》2010年第2期305-312,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60375003);国家航空基金(03I53059)~~

摘　　要：为了精确地描述风险投资商实际的经营状况,本文将一般的Erlang(2)风险模型推广为常利率下有阈红利边界的Erlang(2)风险模型。首先利用全概率公式对风险过程进行分析,得到了模型的罚金折现期望函数所满足的积分-微分方程及积分方程,然后在不带利率时将积分方程简化为"第二类非其次Volterra积分方程",给出了罚金折现期望函数的确切表达式,最后给出了不带利率时模型的破产概率及破产前瞬时盈余和破产赤字的联合分布的表达式。In this paper, in order to describe the actual business venture operating conditions more accurately, we extend the Erlang（2） risk model to the Erlang（2） risk model with a threshold strategy under constant interest. Firstly, the integro-differential equations and the intergral equations satisfied by the expected discounted penalty function are derived by analyzing the risk process and utilizing the total probability formula. Furthermore, the intergral equations are reduced to the second kind of non-homogeneous Volterra integral equations when the interest rate is zero, and the explicit solutions to the integral equations are obtained. Finally, the explicit formulae for the ruin probability and the joint distribution of the surplus immediately before ruin and the deficit at ruin are given in the interest-free case.

关 键 词：ERLANG(2)风险过程 罚金折现期望函数 阈红利边界 积分-微分方程 

分 类 号：O211.9[理学—概率论与数理统计]