Distributions of the surplus before ruin, the deficit at ruin and the claim causing ruin in a class of discrete time risk models

DOI10.1080/03461230510009808zbMath1143.91033OpenAlexW2090814798MaRDI QIDQ3440863

Shuanming Li

Publication date: 29 May 2007

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461230510009808

zbMATH Keywords

Gerber-Shiu functionsurplus before ruindeficit at ruinSparre Andersen risk processcompound geometric distributionclaim causing ruin\(K_m\) family of distributions

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Markov renewal processes, semi-Markov processes (60K15)

Related Items (18)

The finite-time ruin probability under the compound binomial risk model ⋮ Discrete time ruin probability with Parisian delay ⋮ Ruin probability for finite negative binomial mixture claims via recurrence sequences ⋮ Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier ⋮ Discrete risk model revisited ⋮ A threshold-based risk process with a waiting period to pay dividends ⋮ Approximations of the ruin probability in a discrete time risk model ⋮ On a class of renewal risk model with random income ⋮ Discounted aggregate claim costs until ruin in the discrete-time renewal risk model ⋮ On the discounted penalty function in the discrete time stationary renewal risk model ⋮ On a discrete risk model with two-sided jumps ⋮ Discrete Lundberg-type bounds with actuarial applications ⋮ On a discrete-time risk model with general income and time-dependent claims ⋮ On the discounted penalty function in a discrete time renewal risk model with general interclaim times ⋮ On the discrete-time compound renewal risk model with dependence ⋮ Reliability of a Discrete-Time System with Investment ⋮ An approximation of minimum initial capital of investment discrete time surplus process with Weibull distribution in a reinsurance company ⋮ A generalized penalty function for a class of discrete renewal processes

Cites Work

• Ruin probabilities in the compound binomial model
• The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function
• On ruin for the Erlang \((n)\) risk process
• On the distribution of the surplus prior to ruin
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• On the time to ruin for Erlang(2) risk processes.
• On the joint distributions of surplus immediately before ruin and the deficit at ruin for Erlang(2) risk processes.
• Discounted probabilities and ruin theory in the compound binomial model
• The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
• Analysis of a defective renewal equation arising in ruin theory
• A laplace transform representation in a class of renewal queueing and risk processes

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