Statistical Tools for Finance and Insurance  
 

15 Ruin Probabilities in Finite and Infinite Time
15.1 Introduction
15.2 Exact Ruin Probabilities in Infinite Time
15.3 Approximations of the Ruin Probability in Infinite Time
15.3.1 Cramér-Lundberg Approximation
15.3.2 Exponential Approximation
15.3.3 Lundberg Approximation
15.3.4 Beekman-Bowers Approximation
15.3.5 Renyi Approximation
15.3.6 De Vylder Approximation
15.3.7 4-moment Gamma De Vylder Approximation
15.3.8 Heavy Traffic Approximation
15.3.9 Light Traffic Approximation
15.3.10 Heavy-light Traffic Approximation
15.3.11 Subexponential Approximation
15.3.12 Computer Approximation via the Pollaczek-Khinchin Formula
15.3.13 Summary of the Approximations
15.4 Numerical Comparison of the Infinite Time Approximations
15.5 Exact Ruin Probabilities in Finite Time
15.6 Approximations of the Ruin Probability in Finite Time
15.7 Numerical Comparison of the Finite Time Approximations
Bibliography

 
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