Periodic threshold-type dividend strategy in the compound Poisson risk model


Eric Cheung 교수 (University of New South Wales, Australia)

In this talk, the (baseline) surplus process is described by the classical compound Poisson model. Inspired by the idea of periodic dividend decisions in Albrecher, Cheung and Thonhauser (2011), we suppose that at the sequence of time points which are the arrival times of an independent Erlang(n) renewal process, the insurance company observes the surplus level to decide on dividend payments. If the observed surplus level is larger than the maximum of a threshold b and the last observed (post-dividend) level, then a fraction of the excess amount is paid as a lump sum dividend. In this proposed strategy, the surplus process can still have an upward trend with a ruin probability of less than one (as opposed to the barrier strategy in Albrecher, Cheung and Thonhauser (2011)). We are interested in the analysis of the expected discounted dividends before ruin (denoted by V). For general claim size distribution, the solution of V can be derived using defective renewal equations. More explicit result for V is presented when the claim size density has rational Laplace transform. Some numerical results are provided to illustrate the effect of randomized observation times on V and the optimization of V with respect to b under the periodic threshold-type dividend strategy. In particular, the optimal barrier generally depends on the initial surplus level. Convergence to the traditional threshold strategy is also shown as the inter-observation times tend to zero. This is joint work with Zhimin Zhang.