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Recursive Calculation Of Ruin Probabilities At Or Before Claim Instants For Non-Identically Distributed Claims

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  • Raducan, Anisoara Maria
  • Vernic, Raluca
  • Zbaganu, Gheorghita

Abstract

In this paper, we present recursive formulae for the ruin probability at or before a certain claim arrival instant for some particular continuous time risk model. The claim number process underlying this risk model is a renewal process with either Erlang or a mixture of exponentials inter-claim times (ICTs). The claim sizes (CSs) are independent and distributed in Erlang's family, i.e., they can have different parameters, which yields a non-homogeneous risk process. We present the corresponding recursive algorithm used to evaluate the above mentioned ruin probability and we illustrate it on several numerical examples in which we vary the model's parameters to assess the impact of the non-homogeneity on the resulting ruin probability.

Suggested Citation

  • Raducan, Anisoara Maria & Vernic, Raluca & Zbaganu, Gheorghita, 2015. "Recursive Calculation Of Ruin Probabilities At Or Before Claim Instants For Non-Identically Distributed Claims," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 421-443, May.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:02:p:421-443_00
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    Cited by:

    1. Tautvydas Kuras & Jonas Sprindys & Jonas Šiaulys, 2020. "Martingale Approach to Derive Lundberg-Type Inequalities," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    2. 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.
    3. He, Yue & Kawai, Reiichiro, 2022. "Moment and polynomial bounds for ruin-related quantities in risk theory," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1255-1271.
    4. Raluca Vernic, 2017. "Capital Allocation for Sarmanov’s Class of Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 311-330, March.
    5. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.

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