Abstract
We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.
Highlights
The classical Cramér–Lundberg model is a foundational mathematical representation of an insurer’s surplus process in risk theory
We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with a model which generalizes the single threshold-based risk model introduced by Drekic and
We focus on the independent Sparre Andersen model (i.e., α j (k) = α j )
Summary
The classical Cramér–Lundberg model is a foundational mathematical representation of an insurer’s surplus process in risk theory. Bruno de Finetti [1] first introduced the notion of a dividend strategy and the idea of finding an optimal dividend payment strategy for the insurance risk model This was followed by numerous other researchers who further explored the problem in a variety of contexts (for reviews of the area, the interested reader is directed to Albrecher and Thonhauser [2] and Avanzi [3]). We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with a model which generalizes the single threshold-based risk model introduced by Drekic and.
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