Finite time ruin probabilities for tempered stable insurance risk processes
نویسندگان
چکیده
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 thesemodels. This, in particular, applies to the inverse Gaussian processwhen the safety loading is less than one. © 2013 Elsevier B.V. All rights reserved.
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