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Large deviations theorems for optimal investment problems with large portfolios

  • Chu, Ba
  • Knight, John
  • Satchell, Stephen

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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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 211 (2011)
Issue (Month): 3 (June)
Pages: 533-555

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Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:533-555
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  1. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
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  8. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
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