What is the best approximation of ruin probability in infinite time?

Volume 32 / 2005

Krzysztof Burnecki, Pawe/l Miśta, Aleksander Weron Applicationes Mathematicae 32 (2005), 155-176 MSC: 62P05, 60G55. DOI: 10.4064/am32-2-4

Abstract

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.

Authors

  • Krzysztof BurneckiHugo 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
    e-mail
  • Pawe/l MiśtaHugo Steinhaus Center
    for Stochastic Methods
    Institute of Mathematics
    Wrocław University of Technology
    Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Aleksander WeronHugo Steinhaus Center for Stochastic Methods
    Institute of Mathematics
    Wrocław University of Technology
    Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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