## On a risk model with randomized dividend-decision times.(English)Zbl 1282.91164

Summary: 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.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 91G50 Corporate finance (dividends, real options, etc.) 62P05 Applications of statistics to actuarial sciences and financial mathematics
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### References:

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