Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability  

作　　者：Wen Cai CHEN Zhong Xing YE 

机构地区：[1]Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China [2]Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China [3]Department of mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第4期565-576,共12页数学学报（英文版）

基　　金：National Basic Research Program of China (973 Program No.2007CB814903);National Natural Science Foundation of China (No.70671069)

摘　　要：We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.

关 键 词：mean-variance analysis exogenous liability singular second moment matrixes orthogonal transformations dynamic programming methods 

分 类 号：O151.21[理学—数学]