复合二项对偶模型中的周期性分红问题

Abstract

Abstract: In this paper, we discusses the problem of optimal dividend payment in compound binomial dual model with bounded dividend rates and periodic dividend payments. Through transforming the value function, we obtain some properties of the optimal dividend payment strategy, and show that the optimal value function is the unique solution of a discrete HamiltonJacobi-Bellman equation. Meanwhile, a simple algorithm is obtained for the optimal strategy and the optimal value function. According to the properties of the optimal dividend strategy, an upper bound and a lower bound of the optimal value function are derived. Numerical examples are presented to illustrate the transformation method.

Key words: Dual model, Periodic dividend payments, HJB equation, Contraction mapping, Optimal dividend strategy

CLC Number:

O232

You Lingyun, Tan Jiyang, Li Ziqiang, Zhang Hanjun. Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments[J].Acta mathematica scientia,Series A, 2017, 37(4): 751-766.

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[1] De Finetti B. Su un'impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries, 1957, 2:433-443
[2] Borch K. The Mathematical Theory of Insurance. Lexington, MA:Lexington Books, 1974
[3] Borch K. Economics of Insurance. Amsterdam:North-Holland, 1990
[4] Bühlmann H. Mathematical Methods in Risk Theory. New York:Springer-Verlag, 1970
[5] Gerber H U. An Introduction to Mathematical Risk Theory. Philadelphia:University of Pennsylvania, 1979
[6] Avanzi B, Gerber H U. Optimal dividends in the dual model with diffusion. ASTIN Bulletin, 2008, 38(2):653-667
[7] Jin Z, Yin G. Numerical methods for optimal dividend payment and investment strategies of MarkovModulated jump diffusion models with regular and singular controls. Journal of Optimization Theory and Applications, 2013, 159(1):246-271
[8] Liu W, Yuan H L, Hu Y J. The optimal strategy for insurance company under the influence of terminal value. Acta Mathematica Scientia, 2011, 31B(3):1077-1090
[9] Tan J Y, Li C, Li Z Q, Yang X Q, Zhang B C. Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates. Mathematical Methods of Operations Research, 2015, 82:61-83
[10] Tan J Y, Yang X Q, Li Z Q, Cheng Y J. A Markov decision problem in a risk model with interest rate and Markovian environment. Science China Mathematics, 2016, 59(1):191-204
[11] Tan J Y, Yuan P T, Cheng Y J, Li Z Q. An optimal dividend strategy in the discrete Sparre Andersen model with bounded dividend rates. Journal of Computational and Applied Mathematics, 2014, 258:1-16
[12] Wu Y D, Guo J Y. Optimal dividend and dynamic reinsurance strategies with capital injections and proportional costs. Acta Mathematicae Applicatae Sinica, 2012, 28(3):505-524
[13] Zhou M, Guo J Y. Classical risk model with threshold dividend strategy. Acta Mathematica Scientia, 2008, 28B(2):355-362
[14] Zhu J, Chen F. Dividend optimization under reserve constraints for the Cramér-Lundberg model compounded by force of interest. Economic Modelling, 2015, 46:142-156
[15] Yin C, Wen Y, Zhao Y. On the optimal dividend problem for a spectrally positive Lévy process. Astin Bulletin, 2014, 44:635-651
[16] Avanzi B, Cheung E C K, Wong B, Woo J K. On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency. Insurance:Mathematics and Economic, 2013, 52(1):98-113
[17] Avanzi B, Gerber H U, Shiu E S W. Optimal dividends in the dual model. Insurance:Mathematics and Economics, 2007, 41(1):111-123
[18] Gerber H U, Smith N. Optimal dividends with incomplete information in the dual model. Insurance:Mathematics and Economics, 2008, 43(2):227-233
[19] Li B, Wu R. The dividend function in the jump-diffusion dual model with barrier dividend strategy. Applied Mathematics and Mechanics, 2008, 29(9):1239-1249
[20] Ng A C Y. On a dual model with a dividend threshold. Insurance:Mathematics and Economics, 2009, 44(2):315-324
[21] Azcue P, Muler N. Optimal dividend policies for compound Poisson processes:The case of bounded dividend rates. Insurance:Mathematics and Economics, 2012, 51(1):26-42
[22] Fang Y, Wu R. Optimal dividends in the Brownian motion risk model with interest. Journal of Computational and Applied Mathematics, 2009, 29(1):145-151
[23] Tan J Y, Yang X Q. Optimal dividend strategy in compound binomial model with bounded dividend rates. Acta Mathematicae Applicatae Sinica, 2014, 30(4):859-870
[24] Yin C, Yuen K C. Optimality of the threshold dividend strategy for the compound Poisson model. Statistics and Probability Letters, 2011, 81(12):1841-1846
[25] Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model:dividends. ASTIN Bulletin:The Journal of the International Actuarial Association, 2011, 41(2):645-672
[26] Albrecher H, Gerber H U, Shiu E S W. The optimal dividend barrier in the Gamma-Omega model. European Actuarial Journal, 2011, 1(1):43-55
[27] Avanzi B, Tu V, Wong B. On optimal periodic dividend strategies in the dual model with diffusion. Insurance:Mathematics and Economic, 2014, 55:210-224
[28] Tan J Y, Yang X Q. The compound binomial model with a constant dividend barrier and periodically paid dividends. Journal of Systems Science and Complexity, 2012, 25(1):167-177
[29] Choi M C H, Cheung E C K. On the expected discounted dividends in the Cramér-Lundberg risk model with more frequent ruin monitoring than dividend decisions. Insurance:Mathematics and Economics, 2014, 59:121-132
[30] Gerber H U, Shiu E S W, Yang H L. An elementary approach to discrete models of dividend strategies. Insurance:Mathematics and Economics, 2010, 46(1):109-116

Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments

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