Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation

DOI10.1081/STM-200025739zbMath1130.60312OpenAlexW2128516647MaRDI QIDQ3157866

Qi-he Tang

Publication date: 19 January 2005

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/stm-200025739

Mathematics Subject Classification ID

Large deviations (60F10) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Renewal theory (60K05)

Related Items (38)

The finite-time ruin probability for an inhomogeneous renewal risk model ⋮ Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims ⋮ A note on product-convolution for generalized subexponential distributions ⋮ Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk ⋮ Asymptotic Behavior of Random Time Ruin Probability Under Heavy-Tailed Claim Sizes and Dependence Structure ⋮ On the random max-closure for heavy-tailed random variables ⋮ Asymptotic behavior of ruin probabilities in an insurance risk model with quasi-asymptotically independent or bivariate regularly varying-tailed main claim and by-claim ⋮ Uniform asymptotics for the ruin probabilities in a bidimensional renewal risk model with strongly subexponential claims ⋮ Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes ⋮ A large deviation result for aggregate claims with dependent claim occurrences ⋮ Uniform estimate of the finite-time ruin probability for all times in a generalized compound renewal risk model ⋮ Uniform asymptotics of the finite-time ruin probability for all times ⋮ Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest ⋮ Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation ⋮ Approximation of the tail probability of dependent random sums under consistent variation and applications ⋮ Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate ⋮ Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence ⋮ Asymptotic finite-time ruin probabilities in a dependent bidimensional renewal risk model with subexponential claims ⋮ Tails of random sums of a heavy-tailed number of light-tailed terms ⋮ Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities ⋮ Tail behavior of supremum of a random walk when Cramér's condition fails ⋮ Tails of higher-order moments with dominatedly varying summands ⋮ Uniform estimates for the finite-time ruin probability in the dependent renewal risk model ⋮ Local precise large deviations for sums of random variables with \(O\)-regularly varying densities ⋮ Tail behavior of the sums of dependent and heavy-tailed random variables ⋮ Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims ⋮ Tail behaviour of random sums under consistent variation with applications to the compound renewal risk model ⋮ Uniform asymptotics for finite-time ruin probability of a bidimensional risk model ⋮ Asymptotics for randomly weighted and stopped dependent sums ⋮ The uniform local asymptotics for a Lévy process and its overshoot and undershoot ⋮ Asymptotic behaviour of the finite-time ruin probability in renewal risk models ⋮ Uniformly asymptotic behavior for the tail probability of discounted aggregate claims in the time-dependent risk model with upper tail asymptotically independent claims ⋮ Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model ⋮ On preserving the limit points of corresponding objects ⋮ A property of the renewal counting process with application to the finite-time ruin probability ⋮ A note on the uniform asymptotic behavior of the finite-time ruin probability in a nonstandard renewal risk model ⋮ Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims ⋮ Asymptotics of the Finite-time Ruin Probability for the Sparre Andersen Risk Model Perturbed by an Inflated Stationary Chi-process

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