A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

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Article ID: iaor20084520
Country: Netherlands
Volume: 176
Issue: 1
Start Page Number: 423
End Page Number: 434
Publication Date: Jan 2007
Journal: European Journal of Operational Research
Authors: ,
Keywords: programming: integer
Abstract:

In this paper, we consider an extension of the Markovitz model, in which the variance has been replaced with the Value-at-Risk. So a new portfolio optimization problem is formulated. We showed that the model leads to an NP-hard problem, but if the number of past observation T or the number of assets K are low, e.g. fixed to a constant, polynomial time algorithms exist. Furthermore, we showed that the problem can be formulated as an integer programming instance. When K and T are large and αVaR is small – as common in financial practice – the computational results show that the problem can be solved in a reasonable amount of time.

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