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

Andrius Grigutis and Jonas Šiaulys
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Andrius Grigutis: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
Jonas Šiaulys: Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

Mathematics, 2020, vol. 8, issue 2, 1-30

Abstract: 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 ∈ { 1 , 2 , … } , claim Y additionally occurs at even moments of time t ∈ { 2 , 4 , … } and claim Z additionally occurs at every moment of time, which is a multiple of three t ∈ { 3 , 6 , … } . 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 , … } . 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.

Keywords: multi-risk model; discrete-time risk model; ruin probability; survival probability; ultimate time; net profit condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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