On Periodic Dividends for the Classical Risk Model with Debit Interest

Abstract EN

A periodic dividend problem is studied in this paper.

We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored.

First of all, three integro-differential equations for the expected discounted dividends are obtained.

Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims.

A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed.

To demonstrate the existing results, we give some numerical examples.