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The Markov Additive Risk Process Under an Erlangized Dividend Barrier Strategy

  • Zhimin Zhang
  • Eric C. K. Cheung
Article

Abstract

In this paper, we consider a Markov additive insurance risk process under a randomized dividend strategy in the spirit of Albrecher et al. (2011). Decisions on whether to pay dividends are only made at a sequence of dividend decision time points whose intervals are Erlang(n) distributed. At a dividend decision time, if the surplus level is larger than a predetermined dividend barrier, then the excess is paid as a dividend as long as ruin has not occurred. In contrast to Albrecher et al. (2011), it is assumed that the event of ruin is monitored continuously (Avanzi et al. (2013) and Zhang (2014)), i.e. the surplus process is stopped immediately once it drops below zero. The quantities of our interest include the Gerber-Shiu expected discounted penalty function and the expected present value of dividends paid until ruin. Solutions are derived with the use of Markov renewal equations. Numerical examples are given, and the optimal dividend barrier is identified in some cases.

Keywords

Markov additive process Barrier strategy Inter-dividend-decision times Gerber-Shiu function Dividends Markov renewal equation Erlangization 

AMS 2000 Subject Classification

91B30 97M30 60J27 60J75 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing UniversityChongqingPeople’s Republic of China
  2. 2.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongHong Kong

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