an:06900962
Zbl 1398.91350
Nie, Ciyu; Dickson, David C. M.; Li, Shuanming
The finite time ruin probability in a risk model with capital injections
EN
Scand. Actuar. J. 2015, No. 4, 301-318 (2015).
00342978
2015
j
91B30 62P05 60K10
ruin probability; finite time; capital injection
Summary: We consider a risk model with capital injections. We show that in the Sparre Andersen framework the density of the time to ruin for the model with capital injections can be expressed in terms of the density of the time to ruin in an ordinary Sparre Andersen risk process. In the special case of Erlang inter-claim times and exponential claims, we show that there exists a readily computable formula for the density of the time to ruin. When the inter-claim time distribution is exponential, we obtain an explicit solution for the density of the time to ruin when the individual claim amount distribution is Erlang(2), and we explain techniques to find the moments of the time to ruin. In the final section, we consider the related problem of the distribution of the duration of negative surplus in the classical risk model, and we obtain explicit solutions for the (defective) density of the total duration of negative surplus for two individual claim amount distributions.