A DUAL RISK MODEL WITH ADDITIVE AND PROPORTIONAL GAINS: RUIN PROBABILITY AND DIVIDENDS

We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains C-i (i = 1, 2, ... ) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional gain feature; that is, if the surplus process just before the ith arrival is at level u, then for a > 0 the capital jumps up to the level (1 + a)u + C-i. The ruin probability and the distribution of the time to ruin are determined. We furthermore identify the value of discounted cumulative dividend payments, for the case of a Poisson arrival process of proportional gains. In the dividend calculations, we also consider a random perturbation of our basic risk process modeled by an independent Brownian motion with drift.