Optimal dividend and capital injection problem with a random time horizon and a ruin penalty in the dual model

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• 作者：Yong-xia Zhao ; Ding-jun Yao
• 关键词：91B30 ; 93E20 ; dual model ; transaction cost ; dividend ; capital injection ; HJB equation
• 刊名：Applied Mathematics - A Journal of Chinese Universities
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：30
• 期：3
• 页码：325-339
• 全文大小：363 KB
• 参考文献：[1]H Albrecher, S Thonhauser. On optimal dividend strategies in insurance with a random time horizon, In: Advances in Statistics, Probability and Actuarial Science, 2012, 1: 157鈥?80.MathSciNet CrossRef
  [2]B Avanzi, H U Gerber. Optimal dividends in the dual model with diffusion, Astin Bull, 2008, 38(2): 653鈥?67.MATH MathSciNet CrossRef
  [3]B Avanzi, H U Gerber, E S WShiu. Optimal dividends in the dual model, Insurance Math Econom, 2007, 41(1): 111鈥?23.MATH MathSciNet CrossRef
  [4]B Avanzi, J Shen, B Wong. Optimal dividends and capital injections in the dual model with diffusion, Astin Bull, 2011, 41(2): 611鈥?44.MATH MathSciNet
  [5]E Bayraktar, A Kyprianou, K Yamazaki. On optimal dividends in the dual model, Astin Bull, 2013, 43(3): 359鈥?72.MATH CrossRef
  [6]E Bayraktar, A Kyprianou, K Yamazaki. Optimal dividends in the dual model under transaction costs, Insurance Math Econom, 2014, 54: 133鈥?43.MATH MathSciNet CrossRef
  [7]K Borch. The Mathematical Theory of Insurance, Lexington Books, Lexington (Mas- sachusetts), 1974.
  [8]W H Fleming, H M Soner. Controlled Markov Processes and Viscosity Solutions, Stoch Model Appl Probab, Vol 25, Springer, New York, 2006.
  [9]Z Liang, V Young. Dividends and reinsurance under a penalty for ruin, Insurance Math Econom, 2012, 50(3): 437鈥?45.MATH CrossRef
  [10]X Peng, M Chen, J Guo. Optimal dividend and equity issuance problem with proportional and fixed transaction costs, Insurance Math Econom, 2012, 51(3): 576鈥?85.MATH MathSciNet CrossRef
  [11]S Thonhauser, H Albrecher. Dividend maximization under consideration of the time value of ruin, Insurance Math Econom, 2007, 41(1): 163鈥?84.MATH MathSciNet CrossRef
  [12]D Yao, H Yang, R Wang. Optimal financing and dividend strategies in a dual model with proportional costs, J Ind Manag Optim, 2010, 6(4): 761鈥?77.MATH MathSciNet CrossRef
  [13]D Yao, H Yang, R Wang. Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs, European J Oper Res, 2011, 211(3): 568鈥?76.MATH MathSciNet CrossRef
  [14]C Yin, Y Wen, Y Zhao. On the optimal dividend problem for a spectrally positive L茅vy process, Astin Bull, 2014, 635鈥?51.
  [15]Y Zhao, R Wang, D Yao, P Chen. Optimal dividends and capital injections in the dual model with a random time horizon, J Optim Theory Appl, 2014, DOI: 10.鈥?007/鈥媠10957-014-0653-0 .
  
• 作者单位：Yong-xia Zhao (1)
  Ding-jun Yao (2)
  
  1. School of Statistics, Qufu Normal University, Qufu, 273165, China
  2. School of Finance, Nanjing University of Finance and Economics, Nanjing, 210046, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
• ISSN：1993-0445

文摘

In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution. Besides, some numerical examples are presented to illustrate our results. Keywords dual model transaction cost dividend capital injection HJB equation