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Discrete time mean-variance analysis with singular second moment matrixes and an exogenous liability

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Abstract

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 orthogonal 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.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China

    Wen Cai Chen

  2. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, P. R. China

    Wen Cai Chen & Zhong Xing Ye

Authors
  1. Wen Cai Chen
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  2. Zhong Xing Ye
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Correspondence to Wen Cai Chen.

Additional information

Research supported by National Basic Research Program of China (973 Program No. 2007CB814903) and National Natural Science Foundation of China (No. 70671069)

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Chen, W.C., Ye, Z.X. Discrete time mean-variance analysis with singular second moment matrixes and an exogenous liability. Acta. Math. Sin.-English Ser. 24, 565–576 (2008). https://doi.org/10.1007/s10114-007-5261-6

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  • DOI: https://doi.org/10.1007/s10114-007-5261-6

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