Geodesic
What is the best approximation of ruin probability in infinite time?
Krzysztof Burnecki 1   ; Paweł Miśta 2   ; Aleksander Weron 2
1 Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland and Institute of Power Systems Automation Wystawowa 1 51-618 Wrocław, Poland
2 Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland
Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 155-176 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We compare 12 different approximations of ruin probability in infinite time studying typical light- and heavy-tailed claim size distributions, namely exponential, mixture of exponentials, gamma, lognormal, Weibull, loggamma, Pareto and Burr. We show that approximation based on the Pollaczek–Khinchin formula gives most accurate results, in fact it can be chosen as a reference method. We also introduce a promising modification to the De Vylder approximation.
DOI : 10.4064/am32-2-4
Keywords: compare different approximations ruin probability infinite time studying typical light heavy tailed claim size distributions namely exponential mixture exponentials gamma lognormal weibull loggamma pareto burr approximation based pollaczek khinchin formula gives accurate results chosen reference method introduce promising modification vylder approximation

Krzysztof Burnecki  1   ; Paweł Miśta  2   ; Aleksander Weron  2

1 Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland and Institute of Power Systems Automation Wystawowa 1 51-618 Wrocław, Poland
2 Hugo Steinhaus Center for Stochastic Methods Institute of Mathematics Wrocław University of Technology Wyspiańskiego 27 50-370 Wrocław, Poland 
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Krzysztof Burnecki; Paweł Miśta; Aleksander Weron. What is the best approximation of ruin probability in infinite time?. Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 155-176. doi: 10.4064/am32-2-4

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