S. Gerhold

collaborators

4 papers

math.PR2026

On the integrability of the supremum of stochastic volatility models and other martingales

Stefan Gerhold, Julian PachschwÃ¶ll, 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.CA2025

On the supremum of a quotient of power sums

Stefan Gerhold, Friedrich Hubalek

We define a function of two real vectors by a certain homogeneous quotient involving power sums, and show that its supremum grows asymptotically linearly w.r.t. the dimension. From…

math.CV2025

On some inequalities for the two-parameter Mittag-Leffler function in the complex plane

Roberto Garrappa, Stefan Gerhold, Marina Popolizio +1

For the two-parameter Mittag-Leffler function $E_{I^\pm, I^^{2}}$ with $I^\pm > 0$ and $I^^{2} \geq 0,$ we consider the question whether $∣ E_{I^\pm, I^^{2}} (z) ∣$ and $E_{I^\pm, I^^{2}} (ℜ z)$ are comparable on the…

math.PR2025

Unparalleled instances of prolifickness, random walks, and square root boundaries

Stefan Gerhold, Friedrich Hubalek

We revisit the problem of influencing the sex ratio of a population by subjecting reproduction of each family to some stopping rule. As an easy consequence of the strong law of lar…