Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model

Mathematics

Andrius Grigutis¹  Jonas Šiaulys¹ 

[1] Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania;

关键词: multi-risk model;    discrete-time risk model;    ruin probability;    survival probability;    ultimate time;    net profit condition;   

DOI  :  10.3390/math8020147

来源: DOAJ

【 摘 要 】

In this paper, we prove recursive formulas for ultimate time survival probability when three random claims $X,Y,Z$ in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time $t\in \{1,2,\dots \}$ , claim Y additionally occurs at even moments of time $t\in \{2,4,\dots \}$ and claim Z additionally occurs at every moment of time, which is a multiple of three $t\in \{3,6,\dots \}$ . Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form $\{X,X+Y,X+Z,X+Y,X,X+Y+Z,\dots \}$ . Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples.

【 授权许可】

Unknown