Gamma Processes and Finite Time Survival Probabilities

David C. M. Dickson · Howard R. Waters

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Probability and Risk Models Probability and Statistical Research Insurance, Mortality, Demography, Risk Management

Abstract

Abstract In this paper we derive formulae for finite time survival probabilities when the aggregate claims process is a Gamma process. We illustrate how a compound Poisson process can be approximated by a Gamma process and by a process defined as a translated Gamma process. We also show how survival probabilities for a compound Poisson process can be approximated by those for a Gamma process or a translated Gamma process.

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References

1991Risk Theory with the Gamma Process 1991Recursive Calculation of Survival Probabilities 1992The Probability and Severity of Ruin in Finite and Infinite Time 1974The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t)

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2001Analytical Evaluation of Economic Risk Capital for Portfolios of Gamma Risks 2012General theory of geometric Lévy models for dynamic asset pricing 2016The Markov consistency of Archimedean survival processes

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