Abstract
In its origin, the Problem of Moments pertained to powers and trigonometric functions. It was later recognized in the decades of 1950-1970, that the original paradigm was amenable to a substantial and rich generalization performed mainly by Karlin and Kemperman in the West, and Krein (former USSR). This generalization to other sets of functions required the characterization of their positive linear combinations (if any). This extension is linked to a wide range of ideas going from devising economic Quadrature Formulae to the extension of functionals in Banach spaces . In the pricing theory of Mathematical Finance, the center lies in the concept of arbitraging with a probability model behind the prices. (Delbaen and Schachermayer,1994). It is in this context that a more general simile to the problem of moments can be envisaged. The one-period version being an exact parallel to the advanced form of the theory, and useful to unlimited constructions in the finite scenarios setting via Linear Programming (Danzig’s baricentric problems, 1950). In this talk, the problem of ‘The Range of traded Option Prices’ (Davis and Hobson,2007) is viewed from the angle of Moment Theory (MT) and some added features to the solution are exhibited. Some other results arising from MT are also linked to the more recent work ‘Arbitrage bounds for prices of options on realized variance’, Davis, Obloj,Raval, 2011).
[PDF] Slides of the presentation.