Abstract
In this paper, we consider a spectrally negative Levy insurance risk process with a barrier-type dividend strategy. In contrast to the traditional barrier strategy in which dividends are payable to the shareholders immediately when the surplus process reaches a fixed level b (as long as ruin has not yet occurred), it is assumed that the insurer only makes dividend decisions at some discrete time points in the spirit of [ 1 ]. Under such a dividend strategy with Erlang inter-dividend-decision times, expressions for the Gerber-Shiu expected discounted penalty function proposed in [ 24 ] and the moments of total discounted dividends payable until ruin are derived. The results are expressed in terms of the scale functions of a spectrally negative Levy process and an embedded spectrally negative Markov additive process. Our analyses rely on the introduction of a potential measure associated with an Erlang random variable. Numerical illustrations are also given.
Highlights
In this paper, the surplus of an insurance company is modeled by a spectrally negative Levy process X = {Xt}t≥0 described as follows
Any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. ∗ Corresponding author: Zhimin Zhang
For the remainder of the paper, it is assumed that the inter-dividend-decision times are exponentially distributed with mean 1/β, and we consider initial surplus such that X0 = u ∈
Summary
We study the Gerber-Shiu functions and the dividend moments when the inter-dividend-decision times are Erlang(m, β) distributed with density (1.4). M, we let φd,δ,j(u; b) and φw,δ,j(u; b) respectively be the Gerber-Shiu functions (1.6) and (1.7) computed under the same conditions except that the time until the first dividend decision is Erlang(m−j+1, β) distributed.
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