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Information, Model Performance, Pricing And Trading Measures In Incomplete Markets

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  • JINGGANG HUANG

    (Standard & Poor's, 55 Water Street, 46th Floor, New York, NY 10041, USA)

  • SVEN SANDOW

    (Standard & Poor's, 55 Water Street, 46th Floor, New York, NY 10041, USA)

  • CRAIG FRIEDMAN

    (Standard & Poor's, 55 Water Street, 46th Floor, New York, NY 10041, USA)

Abstract

In the incomplete market setting, we define a generalized Kullback-Leibler relative entropy in terms of an investor's expected utility. We motivate, from an economic point of view, this quantity — the relative U-entropy. Relative U-entropy measures the discrepancy from a set of pricing measures to a single probability measure. We show that the relative U-entropy shares a number of important properties with the usual Kullback-Leibler relative entropy, and establish the link between this quantity and the pricing measure corresponding to the least favorable market completion. We also describe an economic performance measure for probabilistic models that may be used by an investor in an incomplete market setting. We then introduce a statistical learning paradigm suitable for investors who learn models and base investment decisions, in an incomplete market, on these models.

Suggested Citation

  • Jinggang Huang & Sven Sandow & Craig Friedman, 2006. "Information, Model Performance, Pricing And Trading Measures In Incomplete Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 373-400.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:03:n:s0219024906003603
    DOI: 10.1142/S0219024906003603
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    References listed on IDEAS

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    1. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
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