Risk processes analyzed as fluid queues

Andrei L. Badescu · Lothar Breuer · Ana da Silva Soares · Guy Latouche · Marie-Ange Remiche · David A. Stanford

86 citations0/0 files storedScandinavian Actuarial Journal

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Probability and Risk Models Probability and Statistical Research Advanced Queuing Theory Analysis

Abstract

This paper presents the Laplace transform of the time until ruin for a fairly general risk model. The model includes both the classical and most Sparre-Andersen risk models with phase-distributed claim amounts as special cases. It also allows for correlated arrival processes, and claim sizes that depend upon environmental factors such as periods of contagion. The paper exploits the relationship between the surplus process and fluid queues, where a number of recent developments have provided the basis for our analysis.

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References

1987Applied Probability and Queues 1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1993A logarithmic reduction algorithm for quasi-birth-death processes 2008Scandinavian Actuarial Journal 1994Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains 1993Marked point processes as limits of Markovian arrival streams 1995Stationary distributions for fluid flow models with or without brownian noise 2023Advances in Queueing Theory, Methods, and Open Problems

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2008First Passage Times for Markov Additive Processes with Positive Jumps of Phase Type 2009Dependent Risk Models with Bivariate Phase-Type Distributions 2007Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier 2006Passage Times in Fluid Models with Application to Risk Processes 2005Phase-type Approximations to Finite-time Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models

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