Supermartingales as Radon-Nikodym densities and related measure extensions

DOI10.1214/14-AOP956zbMath1356.60070arXiv1309.4623MaRDI QIDQ5962535

Johannes Ruf, Nicolas Perkowski

Publication date: 12 February 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4623

zbMATH Keywords

supermartingalesfinitely additive measureCarathéodory extension theoremFatou convergenceFöllmer measureRadon-Nikodym densities

Mathematics Subject Classification ID

Brownian motion (60J65) Generalizations of martingales (60G48) Martingales with continuous parameter (60G44) Probabilistic measure theory (60A10) Stochastic analysis (60H99)

Related Items (19)

Scaled insurance cash flows: representation and computation via change of measure techniques ⋮ Distribution of the time to explosion for one-dimensional diffusions ⋮ Strong supermartingales and limits of nonnegative martingales ⋮ Stochastic exponentials and logarithms on stochastic intervals. A survey ⋮ Symmetries of stochastic differential equations using Girsanov transformations ⋮ Informational Efficiency under Short Sale Constraints ⋮ The existence of dominating local martingale measures ⋮ Bubbles in discrete-time models ⋮ Simplified calculus for semimartingales: multiplicative compensators and changes of measure ⋮ Filtration shrinkage, the structure of deflators, and failure of market completeness ⋮ Absolute continuity of semimartingales ⋮ Pure-jump semimartingales ⋮ Polynomial processes in stochastic portfolio theory ⋮ Financial models with defaultable numéraires ⋮ Convergence of local supermartingales ⋮ On the dual problem of utility maximization in incomplete markets ⋮ Simplified stochastic calculus via semimartingale representations ⋮ Martingale spaces and representations under absolutely continuous changes of probability ⋮ Valuation and Parities for Exchange Options

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