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We study the probability of ruin before time $t$ for the family of temperedstable L\'evy insurance risk processes, which includes the spectrally positiveinverse Gaussian processes. Numerical approximations of the ruin timedistribution are derived via the Laplace transform of the asymptotic ruin timedistribution, for which we have an explicit expression. These are benchmarkedagainst simulations based on importance sampling using stable processes.Theoretical consequences of the asymptotic formulae are found to indicate somepotential drawbacks to the use of the inverse Gaussian process as a riskreserve process. We offer as alternatives natural generalizations which fallwithin the tempered stable family of processes.

Finite Time Ruin Probabilities for Tempered Stable Insurance Risk Processes