随机区间收益金融市场的无强占优分析
The Analysis of Robust Dominant Strategy in the Market with Random Interval Payoffs

作者: 王瑾 , 师恪 :新疆大学,数学与系统科学学院,新疆 乌鲁木齐;

关键词: 随机区间强占优策略线性定价测度Random Interval Robust Dominant Strategy Linear Pricing Measures

摘要: 文章提出了具有随机区间收益的金融市场,在该市场中,证券价格被描述为区间值随机变量,并将研究的金融市场所在的概率空间框架从有限维拓展为一般概率空间,是传统随机市场的推广。在此模型中,提出了强占优策略和线性定价测度的概念,证明了市场无强占优与存在线性定价测度等价的定理,并且研究了随机区间收益市场无强占优与经典市场无占优的关系。该结论既包含经典随机金融市场的结论,又将金融分析推广到随机区间收益金融市场中。

Abstract: In this article, a new financial market model, in which all securities have random interval pay- offs, is proposed. In the market, the probability space from finite dimensional expands general probability space. Some concepts, such as robust dominant strategy and linear pricing measures, are given and discussed parallel to those in traditional market analysis. With these new concepts, it is discussed that the requirement of no robust dominant strategy is equivalent to the existence of linear pricing measures and the relations between the analysis of the no robust dominant strategy in the market with random interval payoffs and it’s in traditional market. This conclusion includes the traditional random market analysis conclusions, extending to this new financial market.

文章引用: 王瑾 , 师恪 (2016) 随机区间收益金融市场的无强占优分析。 统计学与应用, 5, 9-18. doi: 10.12677/SA.2016.51002

参考文献

[1] Follmer, H. and Schied, A. (2004) Stochastic Finance: An Introduction in Discrete Time. Germany.

[2] 雍炯敏, 刘道百. 数学金融学[M]. 上海: 上海人民出版社, 2003.

[3] Muzzioli, S. and Torricelli, C. (2004) A Multiperiod Binomial Model for Pricing Options in a Vague World. Journal of Economic Dynamics & Control, 28, 861-887.
http://dx.doi.org/10.1016/S0165-1889(03)00060-5

[4] Zadeh, L.A. (2005) Toward a Generalized Theory of Uncertainty (GTU)—An Outline. Information Sciences, 172, 1-40.
http://dx.doi.org/10.1016/j.ins.2005.01.017

[5] Lai, K.K., Wang, S.Y. and Xu, J.P. (2002) A Class of Linear In-terval Programming Problems and Its Application to Portfolio Selection. IEEE Transactions on Fuzzy Systems, 10, 698-704.
http://dx.doi.org/10.1109/TFUZZ.2002.805902

[6] Ida, M. (2004) Solutions for the Portfolio Selection Problem with Interval and Fuzzy Coefficients. Reliable Computing, 10, 389-400.
http://dx.doi.org/10.1023/B:REOM.0000032120.83979.d4

[7] Yoshida, Y., Yasuda, M. and Nakagami, J. (2006) A New Evaluation of Mean Value for Fuzzy Numbers and Its Application to American Put Option under Uncertainty. Fuzzy Sets and Systems, 157, 2614-2626.
http://dx.doi.org/10.1016/j.fss.2003.11.022

[8] You, S., Le, J. and Ding, X. (2008) Pricing a Contingent Claim with Random Interval or Fuzzy Random Payoff in One-Period Setting. Original Research Article Computers and Ma-thematics with Applications, 56, 1905-1917.

[9] You, S. and Lei, Q. (2011) Analysis of Expected Utility toward Fuzzy Wealth and Applications in Portfolio Selection. Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD).

[10] You, S. and Shi, J. (2013) On Fair Prices of a Contingent Claim with Random Interval Payoff. Journal of Donghua University (English Edition), 30, 153-157.

[11] You, S. (2013) Pricing and Hedging in a Single Period Market with Random Interval Valued Assets. International Journal of Approximate Reasoning, 54, 1310-1321.
http://dx.doi.org/10.1016/j.ijar.2013.06.002

[12] 魏康. 随机区间损益市场模型下的两种定价方法[D]. 上海: 东华大学, 2015.

[13] 严士健, 王隽骧, 刘秀芳. 概率论基础[M]. 第二版. 科学出版社, 2009.

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