论文标题
具有添加剂和比例收益的双重风险模型：破坏概率和股息
A dual risk model with additive and proportional gains: ruin probability and dividends
论文作者
论文摘要
我们考虑一个双重风险模型，具有恒定的费用率和I.I.D。指数分布的获得$ C_I $（$ i = 1,2，\ dots $），该续签过程中的续签过程与一般的临时时间。我们添加了这个经典的双重风险模型比例增益功能，也就是说，如果$ i $ th到达之前的剩余过程为级别$ u $，那么对于$ a> 0 $，资本将跳至级别$（1+a）u+c_i $。确定破坏的概率和破坏时间的分布。此外，对于托有比例收益的到达过程，我们还确定了折扣累积股息支付的价值。在股息计算中，我们还考虑了我们的基本风险过程的随机扰动，该过程是由独立的布朗尼运动模型的，带有漂移。
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.
