Displaying similar documents to “Properties of set-valued stochastic integrals”

A new proof of Kellerer’s theorem

Francis Hirsch, Bernard Roynette (2012)

ESAIM: Probability and Statistics

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In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.

Elementary stochastic calculus for finance with infinitesimals

Jiří Witzany (2017)

Commentationes Mathematicae Universitatis Carolinae

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The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.