Perturbation Analysis of Sub/Super Hedging Problems

Abstract

We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. Noarbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite-dimensional sub-and super-hedging problems. With a view towards applications, we show how duality is preserved when reducing these problems over finite-dimensional bases. We finally perform a rigorous perturbation analysis of those linear programming problems, and highlight, as a numerical example, the influence of smile extrapolation on the bounds of exotic options.Date: June 12, 2018. 2010 Mathematics Subject Classification. 90C05, 90C46, 91G20, 46N10.

In memoriam: Mark H. A. Davis and his contributions to mathematical finance

“…Among others, Mark worked on interest rates models with V. Mataix‐Pastor (2007, 2009), on sensitivities and Malliavin calculus with M. Johansson (2006) and on risk‐sensitive investment with L. Lleo (2008, 2010, 2011a, 2011b). From the late 2000s, Mark became increasingly interested in model uncertainty and model‐independent methods which led to a string of works, from the paper with D. Hobson (2007), through the work with J. Obłój and V. Raval (2014), to his collaboration with S. Badikov and A. Jacquier (2021), that is included in this volume. These topics also led him to consider pathwise stochastic calculus, Davis et al.…”