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A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processes. (English) Zbl 1401.91147
Summary: We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We consider De Finetti’s problem for one-sided Lévy risk models in both scenarios with and without fix transaction costs. To characterize the solution to the aforementioned models we introduce the dual problem and show that the complementary slackness conditions are satisfied and therefore there is no duality gap. As a consequence the optimal value function can be obtained as the pointwise infimum of auxiliary value functions. Finally, we illustrate our findings with a series of numerical examples.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
93E20 Optimal stochastic control
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