# American Institute of Mathematical Sciences

October  2014, 10(4): 1041-1058. doi: 10.3934/jimo.2014.10.1041

## On a risk model with randomized dividend-decision times

 1 College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

Received  October 2012 Revised  December 2013 Published  February 2014

In this paper, we consider a perturbed compound Poisson risk model with a randomized dividend strategy. Assume that decisions on paying off dividends are made at some random observation times. Whenever the observed value of the surplus process exceeds a given barrier $b$, the excess value will be paid off as dividends. We assume that the Laplace transform of the individual claim size belongs to the rational family. When the time intervals between successive decision times follow exponential distribution, we present explicit expressions for the Gerber-Shiu function. We also extend the exponential assumption to Erlang and discuss the solution procedure.
Citation: Zhimin Zhang. On a risk model with randomized dividend-decision times. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1041-1058. doi: 10.3934/jimo.2014.10.1041
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