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arXiv · 2012.00415

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

Onno Boxma·Esther Frostig·Zbigniew Palmowski
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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.

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Onno Boxma, Esther Frostig, Zbigniew Palmowski. 2020-12-01. A dual risk model with additive and proportional gains: ruin probability and dividends. https://arxiv.org/abs/2012.00415

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