ON THE PROBABILITY OF RUIN IN A CONTINUOUS RISK MODEL WITH DELAYED CLAIMS

Title & Authors
ON THE PROBABILITY OF RUIN IN A CONTINUOUS RISK MODEL WITH DELAYED CLAIMS
Zou, Wei; Xie, Jie-Hua;

Abstract
In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\small{\acute{e}}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.
Keywords
continuous time risk model;survival probability;delayed claim;Laplace transform;
Language
English
Cited by
1.
On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes, Journal of Applied Mathematics, 2014, 2014, 1
2.
THE ULTIMATE RUIN PROBABILITY OF A DEPENDENT DELAYED-CLAIM RISK MODEL PERTURBED BY DIFFUSION WITH CONSTANT FORCE OF INTEREST, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 895
3.
On the probability of ruin in a continuous risk model with two types of delayed claims, Communications in Statistics - Theory and Methods, 2016, 45, 13, 3734
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