Author

Johannes Brutsche

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Open access Oct 2026

The level of self-organized criticality in oscillating Brownian motion: n-consistency and stable Poisson-type convergence of the MLE

For some discretely observed path of oscillating Brownian motion with level of self-organized criticality ρ0, we prove in the infill asymptotics that the MLE is n-consistent, where n denotes the sample size, and derive its limit distribution with respect to stable convergence. As the transition density of this homogene...

Johannes Brutsche, Angelika Rohde · The Annals of Applied Probab... · 0 citations

Preprint Sep 2026

Arbitrage in Estimate Nothing: an example

We give a two-period counterexample to the absence of arbitrage for the posterior-weighted pricing rule in Estimate nothing by Duembgen and Rogers. Both physical models have strictly positive transition densities, and each model is equipped with an equivalent martingale measure. Nevertheless, the mixed price of a singl...

Johannes Brutsche, Julian Sester, Thorsten Schmidt · 0 citations