Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-5

January 1999

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.

Availability: [ gzipped `ps`

-file ] [ `pdf`

-file ]