MPS-RR 1999-5
January 1999

On the ruin problem for some adapted premium rules

Søren Asmussen

Abstract

We consider risk processes where the premium rate $p(t)$ at time $t$ is calculated according to past claims statistics, for example $p(t)=$ $(1+eta) A_{t-}/t$ or $p(t)=$ $(1+eta) (A_{t-}-A_{t-s})/s$ where $eta$ is the safety loading and $A_t$ the total compound Poisson claims in $[0,t]$. We perform a comparison of the ruin probabilities with those of the Cram'er-Lundberg model, and characterize the claims experience leading to ruin. With heavy tails, the controlled risk process has typically at least as large a ruin probability as the Cram'er--Lundberg mod el. With light tails, the adjustment coefficient is typically larger so that the ruin probability is smaller; a key tool is the G"artner--Ellis theorem from large deviations theory. We also consider similar problems for diffusion approximations.

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