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

ABSTRACT

In this paper, the compound Poisson risk model is considered. Inspired by Albrecher, Cheung, & Thonhauser. [(2011b). Randomized observation periods for the compound Poisson risk model: dividend. ASTIN Bulletin 41(2), 645–672], it is assumed that the insurer observes its surplus level periodically to decide on dividend payments at the arrival times of an Erlang(n) renewal process. If the observed surplus is larger than the maximum of a threshold b and the last observed (post-dividend) level, then a fraction of the excess is paid as a lump sum dividend. Ruin is declared when the observed surplus is negative. In this proposed periodic threshold-type dividend strategy, the insurer can have a ruin probability of less than one (as opposed to the periodic barrier strategy). The expected discounted dividends before ruin (denoted by V) will be analyzed. For arbitrary claim distribution, the general solution of V is derived. More explicit result for V is presented when claims have rational Laplace transform. Numerical examples are provided to illustrate the effect of randomized observations on V and the optimization of V with respect to b. When claims are exponential, convergence to the traditional threshold strategy is shown as the inter-observation times tend to zero.

KEYWORDS:

• Compound Poisson model
• expected discounted dividends
• threshold-type dividend strategy
• periodic dividends
• Erlangization

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Eric Cheung gratefully acknowledges the support from the Research Grants Council of the Hong Kong Special Administrative Region (Project Number: 17324016). The research of Zhimin Zhang was supported by the National Natural Science Foundation of China [11471058, 11101451], MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 16YJC910005] and Fundamental Research Funds for the Central Universities (2018CDQYST0016).