The surplus prior to ruin and the deficit at ruin for a correlated risk process

DOI10.1080/03461230510009835zbMath1143.91025OpenAlexW2001718984MaRDI QIDQ5430559

Steve Drekic, David A. Stanford, Andrei L. Badescu, Guy Latouche, Lothar Breuer

Publication date: 16 December 2007

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

Full work available at URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/30182/1/gl-0092.pdf

zbMATH Keywords

phase-type distributionfluid queuesMarkovian arrival processdeficit at ruinSparre Andersen risk modelsurplus immediately prior to ruincorrelated claims

Mathematics Subject Classification ID

Related Items (15)

On the analysis of the Gerber-Shiu discounted penalty function for risk processes with Markovian arrivals ⋮ Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier ⋮ On a perturbed MAP risk model under a threshold dividend strategy ⋮ Erlangian Approximations for the Transient Analysis of a Fluid Queue Model for Forest Fire Perimeter ⋮ The Erlangization method for Markovian fluid flows ⋮ Phase-type approximations perturbed by a heavy-tailed component for the Gerber-Shiu function of risk processes with two-sided jumps ⋮ On the absolute ruin in a MAP risk model with debit interest ⋮ The use of vector-valued martingales in risk theory ⋮ A quintuple law for Markov additive processes with phase-type jumps ⋮ The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model ⋮ Analysis of a threshold dividend strategy for a MAP risk model ⋮ On the analysis of a multi-threshold Markovian risk model ⋮ A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections ⋮ A Risk Model Based on Markov Chains with Marked Transitions ⋮ Analysis of a MAP Risk Model with Stochastic Incomes, Inter-Dependent Phase-Type Claims and a Constant Barrier

Cites Work

• The surpluses immediately before and at ruin, and the amount of the claim causing ruin
• Transient Markov arrival processes
• The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models.
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Erlangian Approximations for Finite-Horizon Ruin Probabilities
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• On the Distribution of the Deficit at Ruin when Claims are Phase-type
• Risk processes analyzed as fluid queues

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