Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence

DOI10.1016/j.insmatheco.2009.08.007zbMath1231.91243OpenAlexW2009456705MaRDI QIDQ659177

Li Wei, Qi-he Tang

Publication date: 10 February 2012

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.insmatheco.2009.08.007

zbMATH Keywords

asymptoticsduality principleconvolution equivalenceHopf factorizationrenewal risk modelWiener

Mathematics Subject Classification ID

Related Items (18)

Lévy insurance risk process with Poissonian taxation ⋮ A note on deficit analysis in dependency models involving Coxian claim amounts ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ Some comparison results for finite-time ruin probabilities in the classical risk model ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ Asymptotic results on tail moment for light-tailed risks ⋮ Potential measures and expected present value of operating costs until ruin in renewal risk models with general interclaim times ⋮ Path decomposition of ruinous behavior for a general Lévy insurance risk process ⋮ Asymptotic results for renewal risk models with risky investments ⋮ Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases ⋮ On the absolute ruin in a MAP risk model with debit interest ⋮ Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims ⋮ The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments ⋮ Mathematical investigation of the Gerber-Shiu function in the case of dependent inter-claim time and claim size ⋮ Finite time ruin probabilities for tempered stable insurance risk processes ⋮ Interplay of insurance and financial risks in a discrete-time model with strongly regular variation ⋮ On corrected phase-type approximations of the time value of ruin with heavy tails ⋮ On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The overshoot of a random walk with negative drift
• On the ruin time distribution for a Sparre Andersen process with exponential claim sizes
• Tail bounds for the joint distribution of the surplus prior to and at ruin
• Tail bounds for the distribution of the deficit in the renewal risk model
• On the discounted penalty function in the renewal risk model with general interclaim times
• On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• Convolution tails, product tails and domains of attraction
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• Degeneracy properties of subcritical branching processes
• Estimation of ruin probabilities by means of hazard rates
• Subexponential distributions and characterizations of related classes
• Functions of probability measures
• The joint distributions of several important actuarial diagnostics in the classical risk model.
• Joint distributions of some actuarial random vectors containing the time of ruin
• The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models.
• The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
• Ruin probabilities and overshoots for general Lévy insurance risk processes
• Characterizations on heavy-tailed distributions by means of hazard rate.
• Analysis of a defective renewal equation arising in ruin theory
• On the Gerber-Shiu discounted penalty function for subexponential claims
• On a class of renewal risk models with a constant dividend barrier
• Overshoots and undershoots of Lévy processes
• On the Constant in the Definition of Subexponential Distributions
• Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation
• A property of the generalized inverse Gaussian distribution with some applications
• Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments
• Convolution equivalence and infinite divisibility
• On The Expected Discounted Penalty function for Lévy Risk Processes
• The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims
• The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model
• Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times
• On a general class of renewal risk process: analysis of the Gerber-Shiu function
• Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process
• The Time Value of Ruin in a Sparre Andersen Model
• Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin Under the Sparre Andersen Model
• On the Time Value of Ruin
• Nonexponential asymptotics for the solutions of renewal equations, with applications

This page was built for publication: Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence