Determining exact survival probability by setting discrete random variables in E. Sparre Andersen’s model  

作　　者：Andrius Grigutis 

机构地区：[1]Institute of Mathematics,Vilnius University,Naugarduko 24,Vilnius,LT-03225,Lithuania

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第4期445-462,共18页概率、不确定性与定量风险（英文）

摘　　要：In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the renewal risk model.More precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))<u),u∈N_(0)using the roots of the probability-generating function,expectation E(X-cθ)X-cθ,and probability mass function of.We assume that the random X_(1),X_(2),...cθ_(1),cθ_(2),...variables of the mutually independent sequences and are cθc>0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and integer.We also assume that the support of is finite.To illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.

关 键 词：Ruin theory Renewal theory Queueing theory Random walk Survival probability Generating function Pollaczek–Khinchine formula Initial values 

分 类 号：O21[理学—概率论与数理统计]