The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times

DOI10.1016/J.AMC.2010.01.068zbMath1202.91129OpenAlexW2113485710MaRDI QIDQ963936

Rong Wu, Min Song, Jiandong Ren, Qing-bin Meng

Publication date: 14 April 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.068

zbMATH Keywords

Markov processphase-type distributiontime of ruinGerber-Shiu discounted penalty functionSparre Anderson risk process

Mathematics Subject Classification ID

Markov renewal processes, semi-Markov processes (60K15)

Related Items (13)

Markov-dependent risk model with multi-layer dividend strategy ⋮ A surplus process involving a compound Poisson counting process and applications ⋮ Lévy Processes, Phase-Type Distributions, and Martingales ⋮ On a Sparre Andersen risk model with time-dependent claim sizes and jump-diffusion perturbation ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ The phase-type risk model perturbed by diffusion under a threshold dividend strategy ⋮ The discounted penalty function with multi-layer dividend strategy in the phase-type risk model ⋮ On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues ⋮ A matrix operator approach to a risk model with two classes of claims ⋮ Dividend Payments in a Risk Model Perturbed by Diffusion with Multiple Thresholds ⋮ On an asymptotic rule \(A+B/u\) for ultimate ruin probabilities under dependence by mixing ⋮ Maximum surplus and \(R_n\) class of distributions with an application to dividends ⋮ On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process

Cites Work

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• On the discounted penalty function in a Markov-dependent risk model
• On ruin for the Erlang \((n)\) risk process
• 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
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• On the expected discounted penalty function at ruin of a surplus process with interest.
• The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models.
• On the time value of absolute ruin with debit interest
• The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion
• The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model
• “The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model”, Jiandong Ren, July 2007
• The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model
• The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model
• The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion
• The time to ruin for a class of Markov additive risk process with two-sided jumps
• The Time Value of Ruin in a Sparre Andersen Model
• On the Time Value of Ruin

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