67 citations · 296 across the 28 of their papers we have counts for
31 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…
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 \(γ\)…
Tractability of -approximation and integration in weighted Hermite spaces of finite smoothness
Gunther Leobacher, Friedrich Pillichshammer, Adrian Ebert
In this paper we consider integration and -approximation for functions over $\RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of sev…
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…
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…
Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift
Gunther Leobacher, Christoph Reisinger, Wolfgang Stockinger
In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-depe…
Zur Irrationalität in der Schule
Gunther Leobacher, Joscha Prochno
Irrational numbers are introduced usually already introduced in lower secondary level schools. But typically, maybe with the exception of , no mathematical proof of irrat…
Independence in Mathematics -- the key to a Gaussian law
Gunther Leobacher, Joscha Prochno
In this manuscript we discuss the notion of (statistical) independence embedded in its historical context. We focus in particular on its appearance and role in number theory, conco…
Change of drift in one-dimensional diffusions
Sascha Desmettre, Gunther Leobacher, L. C. G. Rogers
It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same…
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…
On the length of arcs in labyrinth fractals
Ligia L. Cristea, Gunther Leobacher
Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the fractal is generated…
Supermixed labyrinth fractals
Ligia L. Cristea, Gunther Leobacher
Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in th…
Approximation methods for piecewise deterministic Markov processes and their costs
Peter Kritzer, Gunther Leobacher, Michaela Szölgyenyi +1
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general co…
Numerical methods for SDEs with drift discontinuous on a set of positive reach
Gunther Leobacher, Michaela Szölgyenyi
For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well a…
A short introduction to quasi-Monte Carlo option pricing
Gunther Leobacher
One of the main practical applications of quasi-Monte Carlo (QMC) methods is the valuation of financial derivatives. We aim to give a short introduction into option pricing and sho…
Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
Gunther Leobacher, Michaela Szölgyenyi
We prove strong convergence of order for arbitrarily small of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuo…
On the optimal order of integration in Hermite spaces with finite smoothness
Josef Dick, Christian Irrgeher, Gunther Leobacher +1
We study the numerical approximation of integrals over with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions.…
Utility Indifference Pricing of Insurance Catastrophe Derivatives
Andreas Eichler, Gunther Leobacher, Michaela Szölgyenyi
We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary…
Bayesian Dividend Optimization and Finite Time Ruin Probabilities
Gunther Leobacher, Michaela Szölgyenyi, Stefan Thonhauser
We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm valu…
A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift
Gunther Leobacher, Michaela Szölgyenyi
In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence an…
Fast orthogonal transforms for multi-level quasi-Monte Carlo integration
Christian Irrgeher, Gunther Leobacher
We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example…
Fast Orthogonal transforms for pricing derivatives with quasi-Monte Carlo
Christian Irrgeher, Gunther Leobacher
There are a number of situations where, when computing prices of financial derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to apply an orthogonal transform…
Construction algorithms for plane nets in base
Gunther Leobacher, Friedrich Pillichshammer, Thomas Schell
The class of -nets in base has been introduced by Niederreiter as examples of point sets in the -dimensional unit cube with excellent uniform distribution propertie…
A Numerical Method for SDEs with Discontinuous Drift
Gunther Leobacher, Michaela Szölgyenyi
In this paper we introduce a transformation technique, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient.…