Entropy, a useful concept in risk theory

Abstract

Exponential bounds for ruin probabilities similar to the Lundberg bound e-Ru are considered. They are naturally expressed in terms of the entropy function of the claims distribution. Such bounds are useful because they are easy to calculate numerically, and they are sufficiently accurate for practical purposes. A numerical example from life insurance is presented. The entropy estimates have an interesting structure familiar from thermodynamics, and concepts like “temperature” and “equilibrium” turn out to have relevance in risk theory.

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