Robust portfolio asset allocation and risk measures |
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Authors: | Maria Grazia Scutellà Raffaella Recchia |
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Institution: | (1) PPE Research Centre, Hochschulstrasse 1, 6850 Dornbirn, Austria |
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Abstract: | Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are
not known in advance, but can only be forecast or estimated. Several methodologies have therefore, been proposed to handle
the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem
of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness
is provided by Robust Optimization which, given optimization problems with uncertain parameters, looks for solutions that
will achieve good objective function values for the realization of these parameters in given uncertainty sets. Robust Optimization
thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true,
for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance
portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches,
that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology.
We also give an overview of some of the computational results that have been obtained with the described approaches. In addition
we analyse the relationship between the concepts of robustness and convex risk measures. |
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