serval:BIB_471D4809EE79
On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times
10.1016/j.insmatheco.2005.05.004
000232708000010
Albrecher
H.
author
Claramunt
M.
author
Marmol
M.
author
article
2005
Insurance: Mathematics and Economics
0167-6687
journal
37
2
324-334
In this paper, we present some results on the distribution of dividend payments until ruin under a Sparre Andersen risk model with generalized Erlang(n)-distributed inter-claim times and a constant dividend barrier. An integro-differential equation for the moment-generating function of the sum of the discounted dividend payments until ruin is derived. Moreover, explicit solutions for arbitrary moments of the present value of dividend payments are obtained, when the individual claim amounts have a distribution with rational Laplace transform. Numerical illustrations of the results are given for an Erlang(2) risk model and Erlang(2)-distributed claim amounts.
Renewal risk model
Dividend barrier
Present value of dividend payments
Moment-generating function
eng
60_published
peer-reviewed
University of Lausanne
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