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Locally Constant Model Uncertainty Risk Measure

Author

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  • Obradovic, Lazar

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper introduces a (coherent) risk measure that describes the uncertainty of the model (represented by a probability measure $P_0$) by a set $P_\lambda$ of probability measures each of which has a Radon-Nikodym's derivative (with respect to $P_0$) that lies within the interval $[\lambda,\frac{1}{\lambda}]$ for some constant $\lambda\in(0,1]$. Economic considerations are discussed and an explicit representation is obtained that gives a connection to both the expected loss of the financial position and its *average value-at-risk*. Optimal portfolio analysis is performed -- different optimization criteria lead to Merton portfolio. Comparison with related problems reveals examples of extreme sensitivity of optimal portfolios to model parameters and the choice of risk measure.

Suggested Citation

  • Obradovic, Lazar, 2019. "Locally Constant Model Uncertainty Risk Measure," Center for Mathematical Economics Working Papers 609, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:609
    as

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    File URL: https://pub.uni-bielefeld.de/download/2933748/2933749
    File Function: First Version, 2019
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    References listed on IDEAS

    as
    1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    2. Cheridito, Patrick & Stadje, Mitja, 2009. "Time-inconsistency of VaR and time-consistent alternatives," Finance Research Letters, Elsevier, vol. 6(1), pages 40-46, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Risk measure; Model uncertainty; Value at risk; Average value at risk; Optimal portfolio; Merton portfolio.;
    All these keywords.

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