A dual risk model with additive and proportional gains: ruin probability and dividends

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