Determining exact survival probability by setting discrete random variables in E. Sparre Andersen’s model
作者机构：Institute of MathematicsVilnius UniversityNaugarduko 24VilniusLT-03225Lithuania
出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)
年 卷 期：2023年第8卷第4期
页 面：445-462页
学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学]
主 题：Ruin theory Renewal theory Queueing theory Random walk Survival probability Generating function Pollaczek–Khinchine formula Initial values
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 *** precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and *** also assume that the support of is *** illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.
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