Approximations to ruin probability in the presence of an upper absorbing barrier

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Abstract
Segerdahl (1970) considered a risk process with two absorbing barriers using methods which led to exact solutions for only particular claim amount distributions. The present paper develops an alternative method for exact solutions for ruin probabilities in the presence of an absorbing upper barrier and, by using an embedded Markov chain, obtains numerical approximations for such ruin probabilities for any claim amount distribution. Refinements to the approximating procedure are discussed. Comparison of exact ruin probabilities, when they can be identified, with the corresponding numerical approximations provides a measure of the accuracy of the method. Sensitivity of the method to changes in parameters is illustrated. When explicit exact solutions to ruin probabilities cannot be obtained, it appears likely that accurate approximations can be obtained by the Markov chain approach with less computational effort than is required to carry out numerical solution of the equation(s) for the exact value.

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