Abstract
We consider the perturbed dual risk model with constant interest and a threshold dividend strategy. Firstly, we investigate the moment-generation function of the present value of total dividends until ruin. Integrodifferential equations with certain boundary conditions are derived for the present value of total dividends. Furthermore, using techniques of sinc numerical methods, we obtain the approximation results to the expected present value of total dividends. Finally, numerical examples are presented to show the impact of interest on the expected present value of total dividends and the absolute ruin probability.
Highlights
The classical risk model has been the center of focus for decades
While not very popular in insurance mathematics, this model has appeared in various literature
A similar model was used by Bayraktar and Egami [6] to model the capital of a venture capital investment
Summary
The classical risk model has been the center of focus for decades. In Avanzi et al [1], the authors studied the expected total discounted dividends until ruin for the dual model under the barrier strategy by means of integrodifferential equations. They derived explicit formulas when profits or gains followed an exponential or a mixture of exponential distributions and showed that the optimal value of the dividend barrier under the dual model was independent of the initial surplus. Albrecher et al [12] studied a dual model that paid taxes when the surplus was at a running maximum and calculated the expected total discounted dividends before ruin for exponentially distributed profits. Throughout this paper, we assume that M(u, y; b) and V(u; b) are sufficiently smooth functions in u and y, respectively
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