On a bivariate risk process with a dividend barrier strategy

Abstract

In this paper, we study a continuous-time bivariate risk process in which each individual line of business implements a dividend barrier strategy. The insurance portfolios of the two insurers are correlated as they are subject to common shocks which induce dependent claims. To analyze the expected discounted dividends until the joint ruin time of the bivariate process (i.e. exit from the positive quadrant), we propose a discrete-time counterpart of the model and apply a bivariate extension of the Dickson-Waters discretization (Dickson and Waters (1991)) with the use of a bivariate Panjer type recursion (Walhin and Paris (2000)). Detailed numerical examples under different dependencies via common shocks, copulas and proportional reinsurance are discussed, and applications to optimal problems in reinsurance, capital allocation and dividends are given. It is also illustrated that the optimal pair of dividend barriers maximizing the dividend function is dependent on the initial surplus levels. A modified type of dividend barrier strategy is proposed towards the end.