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The Gerber-Shiu Penalty Function for a Two-sided Renewal Risk Process Perturbed by Diffusion

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  • Ekaterina Todorova Kolkovska

    (Centro de Investigación en Matemáticas)

  • Sonny A. Medina Jimenez

    (University of Bath)

Abstract

We study the Gerber-Shiu discounted penalty function for a renewal risk model with random gains and perturbed by Brownian motion. Here the interarrival times have generalized Erlang distribution, and the process of random gains is a compound Poisson process with exponential jumps. We obtain the Laplace transform and a defective renewal equation for the discounted Gerber-Shiu penalty function, and when the claims have rational distributions, we give explicit expression for this function. An asymptotic result is derived for the probability of ruin when the distribution of claims is heavy-tailed. We provide some numerical results in the final section.

Suggested Citation

  • Ekaterina Todorova Kolkovska & Sonny A. Medina Jimenez, 2025. "The Gerber-Shiu Penalty Function for a Two-sided Renewal Risk Process Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-34, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10152-y
    DOI: 10.1007/s11009-025-10152-y
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    References listed on IDEAS

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    1. Dickson, David C. M. & Hipp, Christian, 1998. "Ruin probabilities for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 251-262, July.
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    6. Kang Hu & Ya Huang & Yingchun Deng, 2023. "Estimating the Gerber–Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion," Mathematics, MDPI, vol. 11(9), pages 1-30, April.
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