On optimal periodic dividend strategies in the dual model with diffusion |
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| Institution: | 1. Risk and Actuarial Studies, Australian School of Business, UNSW Sydney NSW 2052, Australia;2. Département de Mathématiques et de Statistique, Université de Montréal, Montréal (Québec) H3T 1J4, Canada;1. LMAP, Université de Pau, France;2. Department of Mathematics and Statistics, Concordia University, Canada;1. Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C, Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico;2. Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan;1. IEOR Department, Columbia University, NY, USA;2. Department of Mathematics, Universidad de los Andes, Bogotá, Colombia;3. Laboratory of Stochastic Analysis and its Applications, National Research University Higher School of Economics, Moscow, Russia |
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| Abstract: | 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, Bayraktar et al. (2013a) 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. |
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| Keywords: | Optimal dividends Dual model Stochastic control Periodic barrier |
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