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Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. (English) Zbl 0997.91027
This paper studies quadratic portfolio selection problems in a model with finite discrete time and for assets with independent returns whose mean vectors and covariance matrices are known. It gives explicit feedback formulae (in terms of current wealth) for the optimal strategies under several mean-variance related criteria. This is possible because due to the independence assumption, the associated linear-quadratic control problem can be solved explicitly. The paper also gives necessary optimality conditions for maximizing utility from the mean and variance of final wealth, and concludes with a few numerical examples. For related work with a focus more on stochastic optimisation, see also M. C. Steinbach [SIAM Rev. 43, No. 1, 31-85 (2001; Zbl 1049.91086)].

91B28Finance etc. (MSC2000)
49N10Linear-quadratic optimal control problems
93E24Least squares and related methods in stochastic control
90C39Dynamic programming