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A probabilistic approach to the -variation of classical fractal functions with critical roughness
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider Weierstraß and Takagi-van der Waerden functions with critical degree of roughness. In this case, the functions have vanishing variation for all bu…
On the variation of a class of fractal functions
Alexander Schied, Zhenyuan Zhang
The concept of the variation of a continuous function along a refining sequence of partitions is the key to a pathwise Itô integration theory with integrator $f…
On (signed) Takagi-Landsberg functions: variation, maximum, and modulus of continuity
Yuliya Mishura, Alexander Schied
We study a class of signed Takagi-Landsberg functions with Hurst parameter . We first show that the functions in admit a linear $p^{\text…
On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals
Alexander Schied
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex r…