基于随机动力系统的证券市场演化动态研究
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摘要
为刻画异质交易者并存证券市场的演化动态,分析非理性交易者在市场中是否会最终灭绝,建立了一个随机动力系统模型,将新进入者对市场演化长期均衡的影响纳入模型,描述作为开放系统的证券市场演化轨迹。通过对模型的分析,讨论了模型解的存在性和唯一性,分析了市场演化系统的长期发展动态,证明在一定条件下,非理性交易者也可以在市场中长期存在。
Alchian,Friedman and Fama proposed that market participants who pursued the maximum return would survive and profit,and irrational traders would be ultimately eliminated due to long term losses.It was called Market Selection Hypothesis.The law of securities market evolution is analyzed in this paper where rational traders and irrational traders coexist by ideas of biological evolution.A differential dynamic system model,as well as a random dynamic system model,is established to describe a law of stock market evolution.It is discussed whether irrational traders should be eliminated by securities market evolution.The impact of new entrants on securities market evolutionary long-term equilibrium is considered.As well,the existence and uniqueness of the model's solution are discussed.Based on the model,using Ito's lemma,it is proved irrational traders could exit in the long-term under some conditions.Finally the suggested conclusion is verified through numerical simulation.
Alchian,Friedman and Fama proposed that market participants who pursued the maximum return would survive and profit,and irrational traders would be ultimately eliminated due to long term losses.It was called Market Selection Hypothesis.The law of securities market evolution is analyzed in this paper where rational traders and irrational traders coexist by ideas of biological evolution.A differential dynamic system model,as well as a random dynamic system model,is established to describe a law of stock market evolution.It is discussed whether irrational traders should be eliminated by securities market evolution.The impact of new entrants on securities market evolutionary long-term equilibrium is considered.As well,the existence and uniqueness of the model's solution are discussed.Based on the model,using Ito's lemma,it is proved irrational traders could exit in the long-term under some conditions.Finally the suggested conclusion is verified through numerical simulation.
引文
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[2]Friedman M.The case for flexible exchange rates[M].Chicago:University of Chicago Press,1953.
[3]Fama E F.Efficient capital markets:A review of theory and empirical work[J].Journal of Finance,1970,25:383-417.
[4]Blume L,Easley D.Evolution and market behavior[J].Journal of Economic Theory,1992,58:9-40.
[5]Evstigneev I V,Hens T,Schenk-Hoppe K R.Evolutionary stable stock markets[J].Journal of Economic Theory,2006,27:449-468.
[6]杨招军,秦国文.连续进化金融模型与全局渐进化稳定策略[J].经济研究,2006,3:41-49.
[7]龙张红,杨招军,秦国文.基于中国股市的进化金融理论与实证研究[J].金融研究,2007,10:100-110.
[8]Akbas F,Armstrong W J,Sorescu S M,et al.Smart money,dumb money,and capital market anomalies[J].Journal of Finance Economics,2015,118:355-382.
[9]Blume L,Easley D.If you are so smart,why aren’t you rich?Belief selection in complete and in complete markets[J].Econometrica,744(2006):929-966.
[10]Bruno B,Raphael S.Darwinian selection does not eliminate irrational traders[J].European Economic Review,2000,44:469-490.
[11]张永杰,张维,熊熊.投资策略与投资收益:基于计算实验金融的研究[J].管理科学学报,2010,9:107-118.
[12]扈文秀,刘刚,章伟果,等.基于因素嵌入的非理性资产价格泡沫生成生成及膨胀演化研究[J].中国管理科学,2016,5:31-37.
[13]刘燕,朱宏泉.个体与机构投资者,谁左右A股股价变动?[J].中国管理科学,2018,4:120-130.
[14]Shirokikh O,Pastukhov G,Boginski V,et al.Computational study of the US stock market evolution:Arank correlation-based network model[J].Computational Management Science,2013,10:81-103.
[15]Cochrane J H.Presidential address:Discount rate[J].The Journal of Finance,2011,4:1047-1108.
[16]赵鹏举.异质交易者并存证券市场演化动态研究[J],经济经纬,2016,3:156-160.
[17]Lo A W.The adaptive market hypothesis:Markets efficiency from an evolutionary perspective[J].Social Science Electronic Publishing,2004,31(1):21-44.
[18]Oksendal B.随机微分方程导论与应用[M].北京:科学出版社,2012.
[19]Ikeda N,Watanabe S.A comparison theorem for solutions of stochastic differential equations and its applications[J].Osaka Journal of Math,1977,14(3):619-633.
[20]Seather B E,Engen S,Lande R,et al.Estimating the time to extinction in an island population of song sparrows[J].Proceedings of Biological Sciences,2000,267:621-626.
[21]Higham D J.An algorithmic introduction to numerical simulations of stochastic differential equations[J].Siam Review,2001,43(3):525-546.
[2]Friedman M.The case for flexible exchange rates[M].Chicago:University of Chicago Press,1953.
[3]Fama E F.Efficient capital markets:A review of theory and empirical work[J].Journal of Finance,1970,25:383-417.
[4]Blume L,Easley D.Evolution and market behavior[J].Journal of Economic Theory,1992,58:9-40.
[5]Evstigneev I V,Hens T,Schenk-Hoppe K R.Evolutionary stable stock markets[J].Journal of Economic Theory,2006,27:449-468.
[6]杨招军,秦国文.连续进化金融模型与全局渐进化稳定策略[J].经济研究,2006,3:41-49.
[7]龙张红,杨招军,秦国文.基于中国股市的进化金融理论与实证研究[J].金融研究,2007,10:100-110.
[8]Akbas F,Armstrong W J,Sorescu S M,et al.Smart money,dumb money,and capital market anomalies[J].Journal of Finance Economics,2015,118:355-382.
[9]Blume L,Easley D.If you are so smart,why aren’t you rich?Belief selection in complete and in complete markets[J].Econometrica,744(2006):929-966.
[10]Bruno B,Raphael S.Darwinian selection does not eliminate irrational traders[J].European Economic Review,2000,44:469-490.
[11]张永杰,张维,熊熊.投资策略与投资收益:基于计算实验金融的研究[J].管理科学学报,2010,9:107-118.
[12]扈文秀,刘刚,章伟果,等.基于因素嵌入的非理性资产价格泡沫生成生成及膨胀演化研究[J].中国管理科学,2016,5:31-37.
[13]刘燕,朱宏泉.个体与机构投资者,谁左右A股股价变动?[J].中国管理科学,2018,4:120-130.
[14]Shirokikh O,Pastukhov G,Boginski V,et al.Computational study of the US stock market evolution:Arank correlation-based network model[J].Computational Management Science,2013,10:81-103.
[15]Cochrane J H.Presidential address:Discount rate[J].The Journal of Finance,2011,4:1047-1108.
[16]赵鹏举.异质交易者并存证券市场演化动态研究[J],经济经纬,2016,3:156-160.
[17]Lo A W.The adaptive market hypothesis:Markets efficiency from an evolutionary perspective[J].Social Science Electronic Publishing,2004,31(1):21-44.
[18]Oksendal B.随机微分方程导论与应用[M].北京:科学出版社,2012.
[19]Ikeda N,Watanabe S.A comparison theorem for solutions of stochastic differential equations and its applications[J].Osaka Journal of Math,1977,14(3):619-633.
[20]Seather B E,Engen S,Lande R,et al.Estimating the time to extinction in an island population of song sparrows[J].Proceedings of Biological Sciences,2000,267:621-626.
[21]Higham D J.An algorithmic introduction to numerical simulations of stochastic differential equations[J].Siam Review,2001,43(3):525-546.
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