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Numerical solutions to dynamic portfolio problems: The case for value function iteration using Taylor approximation. (English) Zbl 1161.91392

Summary: In a recent paper, J. van Binsbergen and M. W. Brandt [Comput. Econ. 29, No. 3–4, 355–367 (2007; Zbl 1161.91413)], using the method of M. W. Brandt et al. [Rev. Fin. Stud. 18, 831–873 (2005)], argue, in the context of a portfolio choice problem with CRRA preferences, that value function iteration (VFI) is inferior to portfolio weight iteration (PWI), when a Taylor approximation is used. In particular, they report that the value function iteration produces highly inaccurate solutions when risk aversion is high and the investment horizon long. We argue that the reason for the deterioration of VFI is the high nonlinearity of the value function and illustrate that if one uses a natural and economically-motivated transformation of the value function, namely the certainty equivalent, the VFI approach produces very accurate results.

MSC:

91B28 Finance etc. (MSC2000)
65K05 Numerical mathematical programming methods

Citations:

Zbl 1161.91413
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References:

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