Ruin theory with excess of loss reinsurance and reinstatements

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Ruin theory with excess of loss reinsurance and reinstatements
The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical CramerLundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process.
Hansjörg Albrecher, Sandra Haas
Added 24 Aug 2011
Updated 24 Aug 2011
Type Journal
Year 2011
Where AMC
Authors Hansjörg Albrecher, Sandra Haas
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