保费依赖余额模型的最优分红问题
Optimal Dividend Problem for the Risk Model with Surplus-Dependent Premiums
DOI: 10.12677/AAM.2019.84090, PDF,   
作者: 刘 雪：河北工业大学理学院，天津
关键词: 最优分红问题；PDMP；测度值DPE；Optimal Dividend Problem； PDMP； Measure-Valued DPE
摘要: 本文研究了保费依赖余额模型的最优分红问题。目标是最大化破产前的累积期望折现分红，首先，我们给出值函数的基本性质，然后运用测度值生成元的理论得到测度值动态规划方程(测度值DPE)。
Abstract: In this paper, we consider the optimal dividend problem for the risk model with surplus-dependent premiums. The objective is to maximize the expected cumulative discounted dividends payment up to the time of ruin. Firstly, we show the basic properties of the value function. Using the theory of measure-valued generators, we derive the associated measure-valued dynamic programming equation (measure-valued DPE).
文章引用：刘雪. 保费依赖余额模型的最优分红问题[J]. 应用数学进展, 2019, 8(4): 798-804. https://doi.org/10.12677/AAM.2019.84090

参考文献

[1] Costa, O.L.V. and Raymundo, C.A.B. (2000) Impulse and Continuous Control of Piecewise Deterministic Markov Processes. Stochastics: An International Journal of Probability Stochastic Processes, 70, 75-107.
[2] Azcue, P. and Muler, N. (2005) Optimal Reinsurance and Dividend Distribution Policies in the Cramer-Lundberg Model. Mathematical Finance, 15, 261-308. [Google Scholar] [CrossRef] 
[3] Liu, G. and Liu, Z. (2015) Piecewise Deterministic Markov Processes and Additive Functional of Semi-Dynamic Systems. Scientia Sinica Mathematics, 45, 579-592. (In Chinese)
[4] Cai, J., Feng, R. and Willmot, G.E. (2009) On the Expectation of Total Discounted Operating Costs up to Default and Its Applications. Advances in Applied Probability, 41, 495-522. [Google Scholar] [CrossRef] 
[5] Feng, R., Zhang, S. and Zhu, C. (2013) Optimal Dividend Payment Problems in Piecewise-Deterministic Compound Poisson Risk Models. IEEE Decision and Control, 7309-7314.
[6] Marciniak, E. and Palmowski, Z. (2016) On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums. Journal of Optimization Theory Applications, 168, 723-742. [Google Scholar] [CrossRef] 
[7] Schmidli, H. (2008) Stochastic Control in Insurance. Springer, London.
[8] De Finetti, B. (1957) Su un’impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuarie, 2, 433-443.
[9] Azcue, P. and Muler, N. (2014) Stochastic Optimization in Insurance: A Dynamic Programming Approach. In Springer Briefs in Quantitative Finance. [Google Scholar] [CrossRef] 
[10] Liu, Z., Jiao, Y. and Liu, G. (2017) Measured-Valued Generator of General Piecewise Deterministic Markov Processes. arXiv: 1704.00938

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