Convex Comparison of Minimal Divergence Martingale Measures in Discrete Time Models

17 Pages Posted: 20 Jul 2012

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Date Written: July 14, 2012

Abstract

We refine some criteria for the convex comparison of martingale densities suggested in Franke et al. (1999) and Bellini and Sgarra (2012). We give sufficient conditions for comparison based on the classical notion of comparative convexity. We apply these conditions to the case of minimal f-divergence martingale measures, establishing an ordering result in the case of power divergences. We discuss the extension of the comparison to a multiperiod setting and provide several numerical examples.

Keywords: convex comparison, relative convexity, Esscher martingale measure, minimal entropy martingale measure, minimal divergence martingale measure

Suggested Citation

Bellini, Fabio, Convex Comparison of Minimal Divergence Martingale Measures in Discrete Time Models (July 14, 2012). Available at SSRN: https://ssrn.com/abstract=2113976 or http://dx.doi.org/10.2139/ssrn.2113976

Fabio Bellini (Contact Author)

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

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