Finite time ruin probabilities for tempered stable insurance risk processes

Philip S. Griffin, Ross A. Maller and Dale Roberts

Insurance: Mathematics and Economics, 2013, vol. 53, issue 2, 478-489

Abstract: We study the probability of ruin before time t for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations based on importance sampling using stable processes. Theoretical consequences of the asymptotic formulae indicate that some care is needed in the choice of parameters to avoid exponential growth (in time) of the ruin probabilities in these models. This, in particular, applies to the inverse Gaussian process when the safety loading is less than one.

Keywords: Ruin probabilities; Insurance risk; Lévy process; Fluctuation theory; Convolution equivalent; Tempered stable; Inverse Gaussian (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:2:p:478-489

DOI: 10.1016/j.insmatheco.2013.07.010

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