非完全有限维金融市场未定权益定价的度量广义逆方法  

The Method of the Metric Generalized Inverse in the Pricing of Contingent Claims in the Incomplete Financial Market

作　　者：王筱凌 王玉文[2] Wang Xiaoling;Wang Yuwen(Heilongjiang University of Finance and Economic;Harbin Normal University)

机构地区：[1]黑龙江财经学院 [2]哈尔滨师范大学

出　　处：《哈尔滨师范大学自然科学学报》2021年第2期12-16,共5页Natural Science Journal of Harbin Normal University

基　　金：黑龙江自然科学基金项目(LH2019A017)。

摘　　要：讨论在时刻t=0具有n个基本证券的金融市场,到未来t=T市场中基本证券处于m种状态,当时间T足够长时,金融市场一定是非完全的.由基本证券的偿付矩阵定义了从Banach空间l^(n)_(1)到Hilbert空间l^(n)_(2)中有界线性算子A,将未定权益空间l^(n)_(2)中任一不可达元y的定价,转化为从l^(n)_(2)到l^(n)_(1)中集值度量广义逆A■在y处的集合值A■(y)的单值选择,证得A+y恰为其单值选择,其中A+为矩阵A的Moore-Penrose广义逆.In this paper,the finance market with n basic securities is discussed at time t=0,when t=T in the future,each securities will be at m states,provided time T is long enough,the finance market must be incomplete.By means of the payoff matrix of n basic securities,a bounded linear operator A from the Banach space l^(n)_(1)to the Hilbert space l^(n)_(2)could be defined,so that any unreachable element y in the contingent claims space l^(n)_(2)into single value selection for the set-value A■(y)of the set-valued metric generalized inverse from A■the Hilbert space l^(n)_(1)to the Banach space ln1 is converted.It is proved that A+y is just the single value selection,where A+is just the Moore-Penrose inverse.

关 键 词：非完全金融市场 未定权益 度量广义逆 MOORE-PENROSE广义逆 

分 类 号：O29[理学—应用数学]