A Numerical Approach to Ruin Models with Excess of Loss Reinsurance and Reinstatements

The present paper studies some computational challenges for the determination of the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of classical risk theory, a contractive integral operator is studied whose fixed point is the ruin probability of the cedent. We develop and implement a recursive algorithm involving high-dimensional integration to obtain a numerical approximation of this quantity. Furthermore we analyze the effect of different starting functions and recursion depths on the performance of the algorithm and compare the results with the alternative of stochastic simulation of the risk process.