保费和索赔到达率与余额相依的最优有界分红率问题

doi:10.15960/j.cnki.issn.1007-6093.2021.01.003

Operations Research Transactions ›› 2021, Vol. 25 ›› Issue (1): 31-49.doi: 10.15960/j.cnki.issn.1007-6093.2021.01.003

Previous Articles Next Articles

Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates

Xue LIU¹, Jingwei LI², Guoxin LIU¹^,*()

1. School of Science, Hebei University of Technology, Tianjin 300401, China
2. School of Economics and Management, Hebei University of Technology, Tianjin 300401, China

Received:2018-12-10 Online:2021-03-15 Published:2021-03-05
Contact: Guoxin LIU E-mail:gxliu@hebut.edu.cn

Abstract

Abstract:

In this paper, we consider the optimal dividend problem with bounded dividend rate for the risk model with surplus-dependent premiums and surplus-dependent claim arrivals. The objective is to maximize the expected cumulative discounted dividends payment up to the time of ruin. Firstly, we prove that the necessary and sufficient condition for a strategy to be a stationary Markov strategy. Using the the theory of measure-valued generators, we derive the associated measure-valued dynamic programming equation (DPE). Finally, we discuss the relationship between the measure-valued DPE and the corresponding quasi-varational inequalities (QVI), and show that the optimal dividend strategy is a stationary Markov strategy with a band structure.

Key words: optimal dividend problem, PDMP, measure-valued DPE, Markov strategy, band structure

CLC Number:

O211

Xue LIU, Jingwei LI, Guoxin LIU. Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates[J]. Operations Research Transactions, 2021, 25(1): 31-49.

References 12

1	De Finetti B . Su un'impostazione alternativa della teoria collettiva del rischio[J]. Transactions of the XVth International Congress of Actuarie, 1957, 2, 433- 443.
2	Asmussen S , Hojgaard B , Taksar M . Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation[J]. Finance Stochastic, 2000, 4 (3): 299- 324. doi: 10.1007/s007800050075
3	Jgaard B H , Taksar M . Controlling risk exposure and dividends payout schemes: insurance company example[J]. Mathematical Finance, 1999, 9 (2): 153- 182. doi: 10.1111/1467-9965.00066
4	Thonhauser S , Albrecher H . Dividend maximization under consideration of the time value of ruin[J]. Insurance Mathematics Economics, 2007, 41 (1): 163- 184. doi: 10.1016/j.insmatheco.2006.10.013
5	Hans U , Gerber A S A , Elias S W , et al. On optimal dividend strategies in the compound Poisson model[J]. North American Actuarial Journal, 2006, 10 (2): 76- 93. doi: 10.1080/10920277.2006.10596249
6	Asmussen S , Taksar M . Controlled diffusion models for optimal dividend pay-out[J]. Insurance Mathematics Economics, 1997, 20 (1): 1- 15. doi: 10.1016/S0167-6687(96)00017-0
7	Fang Y , Wu R . Optimal dividend strategy in the compound Poisson model with constant interest[J]. Stochastic Models, 2007, 23, 149- 166. doi: 10.1080/15326340601142271
8	Azcue P , Muler N . Optimal dividend policies for compound Poisson processes: The case of bounded dividend rates[J]. Insurance Mathematics Economics, 2012, 51 (1): 26- 42. doi: 10.1016/j.insmatheco.2012.02.011
9	Davis M H A . Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models[J]. Journal of the Royal Statistical Society, 1984, 46 (3): 353- 388.
10	Marciniak E , Palmowski Z . On the optimal dividend problem for insurance risk models with surplus-dependent premiums[J]. Journal of Optimization Theory Applications, 2016, 168 (2): 723- 742. doi: 10.1007/s10957-015-0755-3
11	Feng R , Zhang S , Zhu C . Optimal dividend payment problems in piecewise-deterministic compound Poisson risk models[J]. Decision and Control, 2013, 7309- 7314.
12	Liu Z, Jiao Y, Liu G. Measure-valued generators of general piecewise deterministic Markov processes[J]. 2017, arXiv: 1704.00938v3.

[1]	LIU Hongjian, FEI Weiyin, ZHU Yongwang$, ZHENG Anman. Optimal consumption-portfolio and bequest with insurance and retirement under Knighting uncertainty [J]. Operations Research Transactions, 2014, 18(3): 88-98.
[2]	WU Jintang. Stochastic orders and aging properties on record values [J]. Operations Research Transactions, 2014, 18(2): 103-110.
[3]	LI Ling, CHENG Guoqing. Optimization of shock model being maintained under imperfect inspection [J]. Operations Research Transactions, 2013, 17(4): 33-42.
[4]	YE Fei, WANG Yifei. Extended Viterbi algorithm based on dynamic programming for high-order hidden Markov model [J]. Operations Research Transactions, 2013, 17(4): 43-55.
[5]	HUAGN Ya, WANG Jing, ZHOU Jieming, DENG Yingchun. The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks [J]. Operations Research Transactions, 2019, 23(4): 13-33.

Optimal dividend strategies for surplus-dependent premiums and surplus-dependent claim arrivals rates: the cases of bounded dividend rates

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References 12

Related Articles 5

Recommended Articles

Metrics

Comments