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On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence

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  • Franck Adékambi

    (University of Johannesburg)

  • Essodina Takouda

    (University of Johannesburg)

Abstract

In this paper, we consider the risk model perturbed by a diffusion process. We assume an Erlang(n) risk process, ( $$n=1,2,\ldots$$ n = 1 , 2 , … ) to study the Gerber-Shiu discounted penalty function when ruin is due to claims or oscillations by including a dependence structure between claim sizes and their occurrence time. We derive the integro-differential equation of the expected discounted penalty function, its Laplace transform. Then, by analyzing the roots of the generalized Lundberg equation, we show that the expected penalty function satisfies a certain defective renewal equation and provide its representation solution. Finally, we give some explicit expressions for the Gerber-Shiu discounted penalty functions when the claim size distributions are Erlang(m), ( $$m=1,2,\ldots$$ m = 1 , 2 , … ) and provide numerical examples to illustrate the ruin probability.

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  • Franck Adékambi & Essodina Takouda, 2022. "On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 481-513, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-022-09944-3
    DOI: 10.1007/s11009-022-09944-3
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    References listed on IDEAS

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