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 that induce dependent claims. To analyse 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 discretisation with the use of a bivariate Panjer-type recursion. 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 maximising the dividend function is dependent on the initial surplus levels. A modified type of dividend barrier strategy is proposed towards the end.

A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process

“…Concerning approximations, recursive integral formulas were derived by Dang et al (2009) which were further generalized and probabilistically interpreted by Gong et al (2012) who also transformed these to recursive sums that are easier to compute. Moreover, approximations of continuous-time bivariate models via their discrete-time counterparts were developed by Yuen et al (2006), Castañer et al (2013), and Liu and Cheung (2015). Multi-dimensional Brownian motion risk models have recently been analyzed by e.g.…”

“…For dividend strategies in twodimensional risk processes, see e.g. Czarna and Palmowski (2011), Liu and Cheung (2015), Albrecher et al (2019), Gu et al (2018), Azcue et al (2019), and Grandits (2019). In addition, applications of bivariate ruin probabilities in reinsurance were considered by e.g.…”