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On optimal periodic dividend strategies in the dual model with diffusion. (English) Zbl 1296.91143
Summary: The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, E. Bayraktar et al. [Astin Bull. 43, No. 3, 359–372 (2013; Zbl 1283.91192)] show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.
In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximizes the expected present value of dividends paid until ruin. Interestingly, a ‘liquidation-at-first-opportunity’ strategy is optimal in some cases where the surplus process has a positive drift. Results are illustrated.

MSC:
91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
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