On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims (Communications in Mathematical Research, 2021)
In this paper, we consider a risk model in which two types of individualclaims, main claims and by-claims, are defined. Every by-claim is induced by the mainclaim randomly and may be delayed for one time period with a certain probability.The dividend policy that certain amount of dividends will be paid as long as thesurplus is greater than a constant dividend barrier is also introduced into this delayedclaims risk model. By means of the probability generating functions, formulae for theexpected present value of total dividend payments prior to ruin are obtained fordiscrete-type individual claims. Explicit expressions for the corresponding results arederived for $K_n$ claim amount distributions. Numerical illustrations are also given.
Keywords: compound binomial model; delayed claim; dividend; expected present value.