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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