Pathwise versions of the Burkholder-Davis-Gundy inequality

Abstract

We present a new proof of the Burkholder-Davis-Gundy inequalities for $1\le p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging.

arXiv commentPublished at http://dx.doi.org/10.3150/13-BEJ570 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (5)

• The Skorokhod embedding problem and its offspring
• Arbitrage and duality in nondominated discrete-time models
• Root's barrier: Construction, optimality and applications to variance options
• A trajectorial interpretation of Doob's martingale inequalities
• Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping

Cited by in corpus (9)

• Sample Out-Of-Sample Inference Based on Wasserstein Distance
• On Equivalence of Martingale Tail Bounds and Deterministic Regret Inequalities
• Trajectorial Otto calculus
• Martingale optimal transport in the Skorokhod space
• Martingale Inequalities and Deterministic Counterparts
• Calibration of the Bass Local Volatility model
• On the quadratic variation of the model-free price paths with jumps
• On pathwise counterparts of Doob's maximal inequalities
• A trajectorial approach to relative entropy dissipation of McKean$-$Vlasov diffusions: gradient flows and HWBI inequalities