Convex Comparison of Minimal Divergence Martingale Measures in Discrete Time Models
17 Pages Posted: 20 Jul 2012
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
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