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On Optimality of the Barrier Strategy for the Classical Risk Model with Interest 被引量：2

On Optimality of the Barrier Strategy for the Classical Risk Model with Interest
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摘要 In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended. In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.
作者 Ying Fang Rong Wu
机构地区 Department of Mathematics Department of Mathematics and LPMC
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第1期75-84,共10页 应用数学学报（英文版）
基金 Supported by National Basic Research Program of China (973 Program) (No. 2007CB814905) National Natural Science Foundation of China (No. 10871102,10926161 and 71071088) the Research Fund for the Doctorial Program of Higher Education
关键词 Optimal dividend strategy barrier strategy confluent hypergeometric function INTEREST Optimal dividend strategy, barrier strategy, confluent hypergeometric function, interest
分类号 O211.6 [理学—概率论与数理统计] O225 [理学—运筹学与控制论]
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参考文献18

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同被引文献18

  • 1Gerber H U, Shiu E S W. with Brownian Motion [J] Journal, 2004,8 (1) : 1 - 20.
  • 2Optimal Dividends: Analysis North American Actuarial Gerber H U, Shiu E S W, Smith N. Methods for Estimating the Optimal Dividend Barrier and the Probability of Ruin [J]. Insurance: Mathematics and Economics, 2008,42(1) :243 - 254.
  • 3Hunting M, Paulsen J. Optimal Dividend Policies with Transaction Costs for a Class of Jump-diffusion Processes [J]. Finance and Stochastics, 2013,17(1) : 7a - 106.
  • 4Bo Lijun, Song Renming, Tang Dan, et al. Levy Risk Model with Two-Sided Jumps and a Barrier Dividend Strategy [J]. Insurance: Mathematics and Economics, 2012,50(2) :280 - 291.
  • 5Chen Mi, Peng Xiaofan, Guo Junyi. Optimal Dividend Problem with a Nonlinear Regular-singular Stochastic Control [J ]. Insurance: Mathematics and Economics, 2013,52(3) :448 - 456.
  • 6Hogaard B. Optimal Dynamic Premium Control in Non- life Insurance: Maximizing Dividend Pay-Outs [ J ]. Scandinavian Actuarial Journal, 2002(4):225- 245.
  • 7Gerber H U,Shiu E S W. On the Time Value of Ruin[J]. North American Actuarial Journal, 1998,2 (1) : 48 - 78.
  • 8Willmot G E, Diekson D C M. The Gerber-Shiu Discounted Penalty Function in the Stationary Renewal Risk Model[J]. Insurance: Mathematics and Economics, 2003,32(3) :403 - 411.
  • 9Lin X S,Willmot G E,Drekic S. The Classical Risk Model with a Constant Dividend Barrier: Analysis of Gerber-Shiu Discounted Penalty Function[J]. Insurance.. Mathematics and Economies, 2003,33(3) :551 - 566.
  • 10Yuen K C, Wang Guoiing, Li W K. The Gerher-Shiu Expected Discounted Penalty Function for Risk Processes with Interest and a Constant Dividend Barrier [J ]. Insurance~ Mathematics and Economics, 2007, 40 ( 1 ) : 104- 112.

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Acta Mathematicae Applicatae Sinica
2011年 第1期

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