On the probability of ruin in a continuous risk model with delayed claims
Wei Zou,Jie-Hua Xie +1 more
TLDR
In this article, the authors considered a continuous time risk model in volving two types of dependent claims, namely main claims and by-claims, and derived the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system.Abstract:Β
In this paper, we consider a continuous time risk model in- volving 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 Rouche'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 proba- bility. 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.read more
Citations
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Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest
TL;DR: An insurance risk model perturbed by diffusion with constant force of interest is considered, where each main claim may induce a delayed claim, called a by-claim, which yields a uniformly asymptotic formula for finite-time ruin probability for times in a finite interval.
Journal ArticleDOI
On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
TL;DR: This work focuses on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims, and derives the integral equation satisfied by the expected Discounted Penalty function.
Journal ArticleDOI
Solution of Ruin Probability for Continuous Time Model Based on Block Trigonometric Exponential Neural Network
TL;DR: The results show that the BTENN model can obtain the approximate solution of the ruin probability under the classical risk model and the Erlang(2) risk model at any time point.
Journal ArticleDOI
The ultimate ruin probability of a dependent delayed-claim risk model perturbed by diffusion with constant force of interest
Qingwu Gao,Erli Zhang,Na Jin +2 more
TL;DR: In this article, the authors extended Li's result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.
Journal ArticleDOI
Gerber Shiu Function of Markov Modulated Delayed By-Claim Type Risk Model with Random Incomes
G. Shija,M. J. Jacob +1 more
TL;DR: In this article, the Gerber-Shiu penalty function of a Markov modulated risk model with delayed by-claims and random incomes is analyzed and an explicit expression for the Laplace transform of the expected discounted penalty function is derived.
References
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Journal ArticleDOI
On the time to ruin for Erlang(2) risk processes
TL;DR: In this article, the authors considered a Sparre Andersen risk process for which the claim inter-arrival distribution is Erlang(2) and defined an auxiliary function Ο along the lines of Gerber and Shiu [N. Am. J. Actu.
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On a risk model with dependence between interclaim arrivals and claim sizes
TL;DR: In this paper, an extension to the classical compound Poisson risk model for which the increments of the aggregate claim amount process are independent is considered and the defective renewal equation satisfied by the expected discounted penalty function is derived.
Journal ArticleDOI
A ruin model with dependence between claim sizes and claim intervals
HansjΓΆrg Albrecher,Onno Boxma +1 more
TL;DR: In this article, the authors considered a generalization of the classical ruin model to a dependent setting, where the distribution of the time between two claim occurrences depends on the previous claim size.
Journal ArticleDOI
Analysis of a defective renewal equation arising in ruin theory
X. Sheldon Lin,Gordon E. Willmot +1 more
TL;DR: In this paper, the authors studied the solution of a defective renewal equation, which involves the time of ruin, the surplus immediately before ruin, and the deficit at the moment of ruin.
Exponential behavior in the presence of dependence in risk theory
TL;DR: In this paper, the authors consider an insurance portfolio situation in which there is possible dependence between the waiting time for a claim and its actual size and obtain explicit exponential estimates for infinite and finite-time ruin probabilities in the case of light-tailed claim sizes.
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