The finite-time ruin probability under the compound binomial risk model

被引：19
|
作者：
Li S. [1 ]
Sendova K.P. [2 ]
机构：
[1] Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Victoria
[2] Department of Statistical and Actuarial Sciences, The University of Western Ontario, 1151 Richmond Street North, London
来源：
European Actuarial Journal | 2013年 / 3卷 / 1期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Compound binomial risk model; Duration of negative surplus; Finite time ruin probability; First hitting time; Generalized Lundberg’s equation; Generating function;
D O I：
10.1007/s13385-013-0063-y
中图分类号：
学科分类号：
摘要：
We study the compound binomial ruin model, which is considered to be the discrete analogue of the classical compound Poisson model. Our key result is a simple approach for inverting a generating function whose argument is the discount factor when we know the inverse of the same generating function, which this time has argument that is the solution to Lundberg’s equation. The main idea comes from a result in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) who discuss the classical model. We are then able to derive the probability distribution of the time to ruin and to go beyond the results in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) by deducing the distribution of the first hitting time of a specific level and the duration of the time when the surplus is negative. The paper contains several illustrative examples where specific claim-amount distributions are considered. © 2013, DAV / DGVFM.
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页码：249 / 271
页数：22
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