67 citations · 294 across the 15 of their papers we have counts for
15 papers
Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximatio…
Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift
Kathrin Spendier, Michaela Szölgyenyi
Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this…
Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substa…
A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jum…
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…
An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis
Andreas Neuenkirch, Michaela Szölgyenyi, Lukasz Szpruch
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the di…
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…
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…
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…
Optimal Liquidation under Partial Information with Price Impact
Katia Colaneri, Zehra Eksi, Rüdiger Frey +1
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finit…
Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information
Anton A. Shardin, Michaela Szölgyenyi
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state proce…
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…
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.…
On the Existence of Solutions of a Class of SDEs with Discontinuous Drift and Singular Diffusion
Gunther Leobacher, Michaela Szölgyenyi, Stefan Thonhauser
The classical result by Itô on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift…