Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Qihe Tang

67 citations0/0 files storedJournal of Applied Probability

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Probability and Risk Models Probability and Statistical Research Advanced Queuing Theory Analysis

Abstract

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1987Applied Probability and Queues 2003Applied Probability and Queues 1997Large deviations of heavy-tailed random sums with applications in insurance and finance 2004Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments 2003Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory 1998Ruin probabilities in the presence of heavy-tails and interest rates

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2009Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims 2017Uniform asymptotics for ruin probabilities in a dependent renewal risk model with stochastic return on investments 2016Finite-time and infinite-time ruin probabilities in a two-dimensional delayed renewal risk model with Sarmanov dependent claims 2019Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest 2015Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model

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