A dual risk model with additive and proportional gains: ruin probability and dividends. (8th June 2023)

• Record Type: Journal Article
• Authors: Boxma, Onno; Frostig, Esther; Palmowski, Zbigniew
• Is Part Of: Advances in applied probability. Volume 55:Number 2(2023)
• Page Start: 549
• Page End: 580
• Publication Date: 2023-06-08
• Subjects: Dual risk model -- ruin probability -- time to ruin -- dividend; 60J99 -- 93E20 -- 60G51; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2022.36
• Languages: English
• ISSNs: 0001-8678

Abstract

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 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 i th 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.