The optimal dividend barrier in the perturbed compound Poisson risk model with randomized observation time

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• 作者：Xiao Liu (1)
  Zhenlong Chen (1)
  Ruixing Ming (1)
  
  1. School of Statistics and Mathematics ; Zhejiang Gongshang University ; Hangzhou ; 310018 ; China
  
• 关键词：Barrier strategy ; dividend ; perturbed compound Poisson risk model ; ruin
• 刊名：Journal of Systems Science and Complexity
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：28
• 期：2
• 页码：451-470
• 全文大小：345 KB
• 参考文献：1. Finetti, B (1957) Su unimpostazione alternativa dell teoria collectiva del rischio. Transaction of the 15th International Congress of Actuaries, New York.
  2. Avanzi, B (2009) Strategies for dividend distribution: A review. North American Actuarial Journal 13: pp. 217-251 CrossRef
  3. Albrecher, H, Thonhauser, S (2009) Optimality results for dividend problems in insurance. RACSAM Revista de la Real Academia de Ciencias; Serie A, Matematicas 103: pp. 295-320
  4. Albrecher, H, Cheung, E C K, Thonhauser, S (2009) Randomized observation periods for the compound Poisson risk model: Dividends. Astin Bull 41: pp. 645-672
  5. Albrecher, H, Gerber, H U, Shiu, E S W (2011) The optimal dividend barrier in the Gamma-Omega model. European Actuarial Journal 1: pp. 43-55 CrossRef
  6. Liu, X, Chen, Z L (2014) Dividend problems in the dual model with diffusion and exponentially distributed observation time. Statistics and Probability Letters 87: pp. 175-183 CrossRef
  7. Wang, C L, Liu, X (2014) Dividend problems in the diffusion model with interest and exponentially distributed observation time. Journal of Applied Mathematics.
  8. Kyprianou, E (2006) Introductory Lectures on Fluctuations of L茅vy Processes with Applications. Springer-Verlag, New York
  9. Zhang, Z M (2014) On a perturbed Sparre Andersen risk model with threshold dividend strategy and dependence. Journal of Computational and Applied Mathematics 255: pp. 248-269 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067

文摘

This paper considers the dividend problems in the perturbed compound Poisson risk model. Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived. When the claim is exponentially distributed, explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained. Finally, the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.