On the maximization of financial performance measures within mixture models
Hentati Rania and
Jean-Luc Prigent ()
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Hentati Rania: University of Paris I, CES, Paris, Frankreich
Statistics & Risk Modeling, 2011, vol. 28, issue 1, 63-80
We introduce mixtures of probability distributions to model empirical distributions of financial asset returns. In this framework, we examine the problem of maximizing performance measures. For this purpose, we consider a large class of reward/risk ratios such as the Kappa measures and in particular the Omega ratio. This latter measure is associated to a downside risk measure based on a put component. All these measures can take account of the asymmetry of the probability distribution, which is important when dealing with mixture of distributions. We examine first a fundamental example: the ranking and maximization of Gaussian mixture distributions, according to the Omega performance measure. Then we provide a general result for the maximization of mixture distributions with respect to a very large family of performance measures, including Kappa measures.
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