Sensitivity Analysis of Insurance Risk Models via Simulation.pdfVIP

Sensitivity Analysis of Insurance Risk Mo dels via Simulation y Sren Asmussen Reuven Y Rubinstein revision February Abstract We show how from a single simulation run to estimate the ruin probabilities and their sensitivities derivatives in a classic insurance risk mo del under various distributions of the numb er of claims and the claim size Similar analysis is given for the tail probabilities of the accumulated claims during a xed p erio d We p erform sensitivity analysis with resp ect to b oth distributional and structural parameters of the underlying risk mo del In the former case we use the score function metho d and in the latter a combination of the pushout metho d and the score function We nally show how from the same sample path to derive a consistent estimator of the optimal solution in an optimization problem asso ciated with excessofloss reinsurance Department of Mathematical Statistics University of Lund Box Lund Sweden Email asmusmathslthse y William Davidson Faculty of Industrial Engineering and Management Technion Haifa Israel Telephone Fax Email ierrrietechnionacil WWW httpiewtechnionacilierrrhtml Research supp orted in part by E and J Bishop Research Fund and the Filip Lundb erg Foundation This pap er deals with sensitivity analysis and sto chastic optimization of p erformance mea sures asso ciated with insurance risk mo dels We assume that the claims arrive according to a Poisson pro cess fNt t g with rate and that the claim sizes are iid nonnegative random variables U i with