Jonas Blessing
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Discrete approximation of risk-based prices under volatility uncertainty Open
We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asympt…
Convergence rates for Chernoff-type approximations of convex monotone semigroups Open
We provide explicit convergence rates for Chernoff-type approximations of convex monotone semigroups which have the form $S(t)f=\lim_{n\to\infty}I(\frac{t}{n})^n f$ for bounded continuous functions $f$. Under suitable conditions on the one…
Convergence of infinitesimal generators and stability of convex monotone semigroups Open
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do no…
Nonlinear semigroups and limit theorems for convex expectations Open
Based on the Chernoff approximation, we provide a general approximation result for convex monotone semigroups which are continuous w.r.t. the mixed topology on suitable spaces of continuous functions. Starting with a family $(I(t))_{t\geq …
Convex monotone semigroups and their generators with respect to $Γ$-convergence Open
We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $Γ$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under the s…
Viscous Hamilton-Jacobi equations in exponential Orlicz hearts Open
We provide a semigroup approach to the viscous Hamilton-Jacobi equation. It turns out that exponential Orlicz hearts are suitable spaces to handle the (quadratic) non-linearity of the Hamiltonian. Based on an abstract extension result for …
Nonlinear semigroups built on generating families and their Lipschitz sets Open
Under suitable conditions on a family $(I(t))_{t\ge 0}$ of Lipschitz mappings on a complete metric space, we show that up to a subsequence the strong limit $S(t):=\lim_{n\to\infty}(I(t 2^{-n}))^{2^n}$ exists for all dyadic time points $t$,…