Supermartingales as Radon-Nikodym densities and related measure extensions

Abstract

Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.

Published at http://dx.doi.org/10.1214/14-AOP956 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• On optimal arbitrage
• Why are quadratic normal volatility models analytically tractable?
• The Martingale Property in the Context of Stochastic Differential Equations
• Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps
• Conditioned Martingales

Cited by in corpus (12)

• Strong supermartingales and limits of nonnegative martingales
• The Martingale Property in the Context of Stochastic Differential Equations
• Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps
• Symmetries of Stochastic Differential Equations using Girsanov transformations
• On the dual problem of utility maximization in incomplete markets
• Simplified stochastic calculus via semimartingale representations
• Martingale Property in Terms of Semimartingale Problems
• Simplified calculus for semimartingales: Multiplicative compensators and changes of measure
• A constraint-based notion of illiquidity
• Pure-jump semimartingales
• Projections of scaled Bessel processes
• Absolute Continuity of Semimartingales