serval:BIB_12E2206E1425
On exact solutions for dividend strategies of threshold and linear barrier type in a Sparre Andersen model
10.1017/S0515036100014847
000251701200002
Albrecher
H.
author
Hartinger
J.
author
Thonhauser
S.
author
article
2007
ASTIN Bulletin
0515-0361
journal
37
2
203-233
For the classical Cramer-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.
Sparre Andersen model
Dividend payments
Piece-wise deterministic Markov processes
Ruin probability
eng
60_published
true
peer-reviewed
University of Lausanne
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