数理金融模型中Abel方程与Bernoulli方程周期问题的等价性  

Equivalence of Abel and Bernoulli Equation Periodic Problem in Mathematical Financial Model

作　　者：孙少卿[1] 孙长军[2] SUN Shao-qing;SUN Chang-jun(College of Finance and Statistics,Hunan University,Changsha 410079,China;Foundation Department,Lianyungang Technical College,Linyungang 222006,China)

机构地区：[1]湖南大学金融与统计学院,湖南长沙410079 [2]连云港职业技术学院基础部,江苏连云港222006

出　　处：《数学的实践与认识》2020年第7期219-223,共5页Mathematics in Practice and Theory

摘　　要：近年来随机微分方程在数理金融中的应用越来越得到人们的重视,而微分方程的周期性研究对经济模型也越来越重要,Abel(阿贝尔)、Bernoulli(伯努利)方程的周期性具有一定的指导性,但周期性问题的研究常具有一定的难度,为了解决这个问题,采用Mironenko发明的反射函数理论,通过构造与Abel方程、Bernoulli方程共同特征的更一般的方程,得到它们的反射函数,研究了Abel方程与Bernoulli方程的等价性,通过Poincare映射得出了它们相同的周期解问题.In recent years,people pay more and more attention to the application of stochastic differential equation in mathematical finance,and the periodicity research of differential equation is more and more important to economic model.The periodicity of Abel(Abel) and Bernoulli(Bernoulli) equation has certain guidance,but the research of periodicity problem often has certain difficulty.In order to solve this problem,Mironenko is adopted in this paper The theory of reflection function is invented.By constructing more general equations with common characteristics with Abel Equation and Bernoulli equation,their reflection function is obtained.The equivalence between Abel Equation and Bernoulli equation is studied.The same periodic solution problem is obtained by Poincare mapping.

关 键 词：反射函数 ABEL方程 BERNOULLI方程 周期问题 等价性 

分 类 号：O211.63[理学—概率论与数理统计] F832[理学—数学]