Large deviations theorems for optimal investment problems with large portfolios

Large deviations theorems for optimal investment problems with large portfolios

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Article ID: iaor20112789
Volume: 211
Issue: 3
Start Page Number: 533
End Page Number: 555
Publication Date: Jun 2011
Journal: European Journal of Operational Research
Authors: , ,
Keywords: portfolio management, hedge funds
Abstract:

The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two‐assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.

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