A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes

This article considers the problem of evaluating
infinite-time (or finite-time) ruin probability under a given compound
Poisson surplus process by approximating the claim size distribution
by a finite mixture exponential, say Hyperexponential, distribution. It
restates the infinite-time (or finite-time) ruin probability as a solvable
ordinary differential equation (or a partial differential equation).
Application of our findings has been given through a simulation study.

Authors:

• Amir T. Payandeh Najafabadi

Keywords:

• Ruin probability
• compound Poisson processes
• mixture exponential (hyperexponential) distribution
• heavy-tailed distributions.

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