Dividend problems in the dual model with diffusion and exponentially distributed observation time |
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| Institution: | 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China;1. Institute of Finance and Development, Nankai University, Tianjin 300071, China;2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China;3. School of Business, Nankai University, Tianjin 300071, China;1. Division of Biostatistics and Epidemiology, University of Massachusetts, Amherst, MA 01003, USA;2. Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA;1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;2. Institut Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67084 Strasbourg cedex, France;3. Department of Mathematical Statistics and Actuarial Science, University of the Free State, 205 Nelson Mandela drive, Park West, 9300 Bloemfontein, South Africa;1. Mathematics Research Unit, University of Luxembourg, Campus Kirchberg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Grand-Duchy of Luxembourg, Luxembourg;2. Faculté des Sciences de Tunis, Campus Universitaire 2092 - El Manar Tunis, Tunisie;1. Department of Mathematics, Tsinghua University, China;2. Institute of Applied Mathematics, AMSS, CAS, Beijing, China;1. University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland;2. Université de Lyon, F-69622 Lyon, France;3. Université Lyon 1, Laboratoire SAF, EA 2429, Institut de Science Financière et d’Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France |
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| Abstract: | Consider dividend problems in the dual model with diffusion and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time, that is, on each observation, if the surplus exceeds the barrier, the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted sum of dividends paid until ruin and the Laplace transform of ruin time are derived. When the gains are exponentially distributed, explicit expressions for the ruin probability, the expected discounted sum of dividends paid until ruin, the Laplace transform of ruin time and the expectation of ruin time are also obtained. |
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| Keywords: | Dividend Ruin Barrier strategy |
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