股票收益率的信息几何

Information Geometry of Stock Return Process

基于信息几何建立股票收益率满足的概率分布族所构成的微分流形,给出流形的几何结构.算出流形的Fisher信息矩阵及其α-联络系数,获得流形在α-联络下的高斯曲率.由流形的α-测地线方程,求出α=0时的解.得到流形的α-散度,-αKullback散度及J-散度,并说明两种散度之间的关系以及各种特殊情况下的散度.

Abstract： Constructs the differential manifold of stock return process based on information geometry, and gives its geometric structure such as the Fisher metric matrix and α-connection coefficients. The Gauss curvature and α-geodesic of the manifold are obtained in the sense of corresponding α- connection. Solution of the geodesic equation when α = 0 is thereby given. Also the α-divergence, α- Kullback divergence and J-divergence of the manifold are given, whilst the relation between the α- divergence and α-Kullback divergence are shown and the divergences in some special cases are given too.