Bivariate Laguerre series approach to insurance risk models: Joint ruin probability and finite-time ruin probability

Seminar in Insurance and Economics

SPEAKER: Eric C.K. Cheung (UNSW Sidney).

TITLE: A Simple Lifecycle Strategy that Requires No Rebalancing.

ABSTRACT: In this presentation, we first consider a two-dimensional insurance risk model where each business line faces not only stand-alone claims but also common shocks that induce dependent losses to both lines simultaneously. The joint ruin probability is analyzed, and under certain assumptions it is shown to be a Schwartz function that can be expressed as a bivariate Laguerre series. In particular, the Laguerre coefficients satisfy a system of linear equations. The key to our derivations relies on the nice analytic properties of bivariate Laguerre series regarding differentiation and convolution, which can be utilized to solve a partial integro-differential equation. The computational procedure is easy to implement, and our numerical examples illustrate its excellent performance. The results are then used to address a related capital allocation problem. If time permits, we also demonstrate that the same methodology can be applied to obtain the finite-time ruin probability in the (univariate) compound Poisson risk model, where exact solutions are typically available only in special cases when the claims follow exponential or more generally mixed Erlang distribution. Claim distributions such as generalized inverse Gaussian, Weibull and truncated normal can be considered using our approach. 

The presentation is based on joint works with Hansjoerg Albrecher, Hayden Lau, Haibo Liu, Gordon Willmot, and Jae-Kyung Woo.

Link to Seminar in Insurance and Economics.