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math.PR2025
Concentration inequalities for strong laws and laws of the iterated logarithm
Johannes Ruf, Ian Waudby-Smith
We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large…
math.PR2024
On the integrability of the supremum of stochastic volatility models and other martingales
Stefan Gerhold, Julian Pachschwöll, Johannes Ruf
We propose a method to bound the expectation of the supremum of the price process in stochastic volatility models. It can be applied, for example, to the rough Bergomi model, avoid…
math.PR2015
Weak Tail Conditions for Local Martingales
Hardy Hulley, Johannes Ruf
The following conditions are necessary and sufficient for an arbitrary càdlàg local martingale to be a uniformly integrable martingale: (i) The weak tail of the supremum of its mod…