Article ID: | iaor20013866 |
Country: | United Kingdom |
Volume: | 52 |
Issue: | 1 |
Start Page Number: | 71 |
End Page Number: | 81 |
Publication Date: | Jan 2001 |
Journal: | Journal of the Operational Research Society |
Authors: | Vzquez-Abad Felisa J., LeQuoc P. |
Keywords: | decision theory, simulation |
The surplus process of an insurance portfolio is defined as the wealth obtained by the premium payments minus the reimbursements made at the time of claims. When this process becomes negative (if ever), we say that ruin has occurred. The general setting is the Gambler's Ruin Problem. In this paper we address the problem of estimating derivatives (sensitivities) of ruin probabilities with respect to the rate of accidents. Estimating probabilities of rare events is a challenging problem, since naïve estimation is not applicable. Solution approaches are very recent, mostly through the use of importance sampling techniques. Sensitivity estimation is an even harder problem for these situations. We shall study three methods for estimating ruin probabilities: one via importance sampling (IS), and two others via indirect simulation: the storage process (SP), which restates the problems in terms of a queuing system, and the convolution formula (CF). To estimate the sensitivities, we apply the Rare Perturbation Analysis (RPA) method to IS, the Infinitesimal Perturbation Analysis (IPA) method to SP and the score function method to CF. Simulation methods are compared in terms of their