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.
In the second part of the talk, we demonstrate that the same methodology can also 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.
|About the speaker||
Dr. Eric Cheung is currently an Associate Professor in the School of Risk and Actuarial Studies of UNSW Sydney. He worked at the University of Hong Kong as an Assistant/Associate Professor for 7 years prior to joining UNSW in 2017. Dr. Cheung's research interests include insurance risk theory, ruin theory, aggregate claims analysis, queueing theory and stochastic processes, and he has published more than 40 papers in these areas. He has the record of securing research grants from national funding agencies in Hong Kong and Australia and from actuarial organizations such as the Society of Actuaries and the Casualty Actuarial Society. He is an Associate of the Society of Actuaries, and he has been an Associate Editor of the leading actuarial journal Insurance: Mathematics and Economics since July 2019.