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

Author

Listed:
  • Andrius Grigutis

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    Both authors contributed equally to this work.)

  • Jonas Šiaulys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    Both authors contributed equally to this work.)

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.

Suggested Citation

  • Andrius Grigutis & Jonas Šiaulys, 2020. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model," Mathematics, MDPI, vol. 8(2), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:147-:d:311412
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    References listed on IDEAS

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