马尔科夫调节风险模型下的最优投资策略:最大化终端效用(英文) 被引量：1

Optimal Investment Strategy in a Markov-Modulated Risk Model:Maximizing the Terminal Utility

下载PDF

导出

摘要本文用跳–扩散模型模拟保险公司的盈余过程,并允许该盈余在由1个无风险资产和N个风险资产组成的金融市场上进行投资.盈余过程和资产价格过程模型中的参数皆受到一个可观察的有限状态连续马尔科夫过程的影响.为了最大化终端效用,我们寻找最优的投资策略,借助HJB方程等工具问题得到解决.当公司的效用函数为指数型时,我们给出了最优投资策略与其对应的值函数的显示表达式,以及相关的经济解释.Browne(1995)和Yang和Zhang(2005)的一些结论得到推广. In this paper, the surplus of an insurance company is governed by a jump-diffusion process, and it can be invested in a financial market with one risk-free asset and N risky assets. The parameters of surplus process and the asset price processes depend on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. To maximize the terminal utility, we focus on finding optimal investment strategy and solve it by using the HJB equation. Explicit expression for optimal strategy and the corresponding objective function are presented when the company has an exponential utility function, some interesting economic interpretations are involved. Some known results of Browne （1995） and Yang and Zhang （2005） are extended.

作者姚定俊钱林义程恭品

机构地区南京财经大学金融学院华东师范大学金融与统计学院中国药科大学理学院

出处《应用概率统计》 CSCD 北大核心 2013年第3期317-329,共13页 Chinese Journal of Applied Probability and Statistics

基金 supported by National Natural Science Foundation of China(11101205,71071071) a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD) Shanghai Municipal Natural Science Foundation(12ZR1408300) Humanity and Social Science Youth Foundation of Ministry of Education of China(12YJC910006) the Fundamental Research Funds for the Central Universities

关键词马尔科夫调节风险模型最优投资策略终端值效用函数 HJB方程 Markov-modulated risk model, optimal investment strategy, terminal wealth, utility function, HJB equation.

分类号 O211.62 [理学—概率论与数理统计]

引文网络
相关文献

参考文献1

1Xin ZHANG,Tak Kuen SIU.On Optimal Proportional Reinsurance and Investment in a Markovian Regime-Switching Economy[J].Acta Mathematica Sinica,English Series,2012,28(1):67-82. 被引量：8

二级参考文献20

1Rabehasaina, L., Sericola, B.: A second-order Markov-modulated fluid queue with linear service rate. J. Appl. Probab., 41, 758-777 (2004).
2Lu, Y., Li, S.: On the probability of ruin in a Markov-modulated risk model. Insurance Math. Econom., 37(3), 522-532 (2005).
3Karatzas, I., Shreve, S. E.: Methods of Mathematical Finance, Springer-Verlag, New York, 2001.
4Elliott, R. J., Aggoun, L., Moore, J.: Hidden Markov Models: Estimation and Control, Springer-Verlag, Berlin-Heidelberg-New York, 1994.
5Browne, S.: Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math. Oper. Res., 20(4), 937-958 (1995).
6Schmidli, H.: Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuar. J., 2001(1), 55-68 (2001).
7Promislow, S. D., Young, V. R.: Minimizing the probability of ruin when claims follow Brownian motion with drift, g. Am. Actuar. J., 9(3), 109-128 (2005).
8Zhang, X., Zhou, M., Guo, J.: Optimal combinational quota-share and excess-of-loss reinsurance policies in a dynamic setting. Appl. Stoch. Models Bus. Ind., 23(1), 63-71 (2002).
9Gerber, H. U., Shiu, E. S. W.: Optimal dividends: analysis with Brownian motion. N. Am, Actuar. J,, 8(1), 1-20 (2OO4).
10Asmussen, S.: Risk theory in a Markovian environment. Scand. Ac$uar. J., 1989, 69-100 (1989).