Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence

Franck Adekambi and Essodina Takouda
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Essodina Takouda: School of Economics, University of Johannesburg, Johannesburg 2006, South Africa

Risks, 2020, vol. 8, issue 1, 1-25

Abstract: This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized mixed equilibrium distribution, we derive the integro-differential Equations of the Gerber–Shiu function and its defective renewal equations. For the situation where claim amounts follow exponential distribution, we provide an explicit expression of the Gerber–Shiu function. Numerical examples are provided to illustrate the ruin probability.

Keywords: ruin theory; delay renewal risk process; renewal equation; convolution formula; diffusion process; FGM copula; exponential and equilibrium distribution. (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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