11 citations · 27 across the 20 of their papers we have counts for
22 papers
A dice game, a multinomial walk, and the inverted Dirichlet distribution
Gunther Leobacher, Alexander Steinicke
We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities…
Locally Lipschitz Path Dependent FBSDEs with Unbounded Terminal Conditions in Brownian and L{é}vy Settings
Hannah Geiss, Céline Labart, Adrien Richou +1
This paper is dedicated to the analysis of forward backward stochastic differential equations driven by a L{é}vy process. We assume that the generator and the terminal condition ar…
Measure and dimension theory of permeable sets and its applications to fractals
Gunther Leobacher, Tapio Rajala, Alexander Steinicke +1
We study {\it permeable} sets. These are sets \(Θ\subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(γ\)…
Worst-Case Optimal Investment in Incomplete Markets
Sascha Desmettre, Sebastian Merkel, Annalena Mickel +1
We study and solve the worst-case optimal portfolio problem as pioneered by Korn and Wilmott (2002) of an investor with logarithmic preferences facing the possibility of a market c…
Product formulas for multiple stochastic integrals associated with Lévy processes
Paolo Di Tella, Christel Geiss, Alexander Steinicke
In the present paper, we obtain an explicit product formula for products of multiple integrals w.r.t. a random measure associated with a Lévy process. As a building block, we use a…
Deviation frequencies of Brownian path property approximations
Michael A. Högele, Alexander Steinicke
This case study proposes a.s.~convergence quantifications of many classical sample path property approximations of Brownian motion in terms of the tradeoff between a.s.~rates and t…
Complements and Improvements Regarding Distributivity of the Product for -Algebras with Respect to the Intersection
K. P. S. Bhaskara Rao, Alexander Steinicke
We present a variety of refined conditions for algebras (on a set ), (on a set ) such that the distributivity equation $$(\mathca…
Continuous functions with impermeable graphs
Zoltán Buczolich, Gunther Leobacher, Alexander Steinicke
We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1…
A Skorohod measurable universal functional representation of solutions to semimartingale SDEs
Paweł Przybyłowicz, Verena Schwarz, Alexander Steinicke +1
In this paper we show the existence of a universal Skorohod measurable functional representation for a large class of semimartingale-driven stochastic differential equations. For t…
Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate
Julia Eisenberg, Stefan Kremsner, Alexander Steinicke
We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a determin…
On the Configurations of Closed Kinematic Chains in three-dimensional Space
Gerhard Zangerl, Alexander Steinicke
A kinematic chain in three-dimensional Euclidean space consists of links that are connected by spherical joints. Such a chain is said to be within a closed configuration when i…
Exception sets of intrinsic and piecewise Lipschitz functions
Gunther Leobacher, Alexander Steinicke
We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The…
A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics
Stefan Kremsner, Alexander Steinicke, Michaela Szölgyenyi
In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilin…
(Non-)Distributivity of the Product for -Algebras with Respect to the Intersection
Alexander Steinicke
We study the validity of the distributivity equation $$(\mathcal{A}\otimes\mathcal{F})\cap(\mathcal{A}\otimes\mathcal{G})=\mathcal{A}\otimes\left(\mathcal{F}\cap\mathcal{G}\right),…
On a combinatorial problem in the Secret Santa ritual
Alexander Steinicke, Markus Penz, Bine Penz
The Secret Santa ritual, where in a group of people every member presents a gift to a randomly assigned partner, poses a combinatorial problem when considering the probabilities in…
-Solutions and Comparison Results for Lévy Driven BSDEs in a Monotonic, General Growth Setting
Stefan Kremsner, Alexander Steinicke
We present a unified approach to -solutions () of multidimensional backward stochastic differential equations (BSDEs) driven by Lévy processes and more general filtrati…
Existence, Uniqueness and Regularity of the Projection onto Differentiable Manifolds
Gunther Leobacher, Alexander Steinicke
We investigate the maximal open domain on which the orthogonal projection map onto a subset can be defined and study essential proper…
Existence, Uniqueness and Malliavin Differentiability of Lévy-driven BSDEs with locally Lipschitz Driver
Christel Geiss, Alexander Steinicke
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a Lévy process. In particular, we are interested i…
Existence, Uniqueness and Comparison Results for BSDEs with Lévy Jumps in an Extended Monotonic Generator Setting
Christel Geiss, Alexander Steinicke
We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a Lévy process. The cons…
Malliavin derivative of random functions and applications to Lévy driven BSDEs
Christel Geiss, Alexander Steinicke
We consider measurable where belongs for any to the Malliavin Sobolev space (with respect to a Lévy pr…
Functionals of a Lévy Process on Canonical and Generic Probability Spaces
Alexander Steinicke
We develop an approach to Malliavin calculus for Lévy processes from the perspective of expressing a random variable by a functional mapping from the Skorohod space of càdl…
-variation of Lévy driven BSDEs with non-smooth terminal conditions
Christel Geiss, Alexander Steinicke
We consider the -regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measu…