B. Robinson, M. Szölgyenyi: Bicausal optimal transport for SDEs with irregular coefficients. Submitted, arXiv:2403.09941, 2024
P. Przybyłowicz, V. Schwarz, M. Szölgyenyi: Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift. Submitted, arXiv:2303.05945, 2023
M. Hitz, M. Szölgyenyi: On the closest pair of points problem. 2022
Publications (peer reviewed)
P. Przybyłowicz, V. Schwarz, M. Szölgyenyi: A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient. Journal of Mathematical Analysis and Applications, 538(1):128319, 2024
P. Przybyłowicz, V. Schwarz, A. Steinicke, M. Szölgyenyi: A Skorohod measurable universal functional representation of solutions to semimartingale SDEs. To appear in Stochastic Analysis and Applications, arXiv:2201.06278, 2024
P. Przybyłowicz, V. Schwarz, M. Szölgyenyi: Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs. Journal of Computational and Applied Mathematics, 440(115631), 2024
K. Spendier, M. Szölgyenyi: Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift. To appear in A. Hinrichs, P. Kritzer, F. Pillichshammer (eds.): Monte Carlo and Quasi-Monte Carlo Methods 2022, arXiv:2212.08839, 2023
J. Hofmeister, D. Kollosche, M. Szölgyenyi: Das Handy versichern? Risikotheorie in der Schule. Mathematik im Unterricht, 14(1-5), 2023
A. Neuenkirch, M. Szölgyenyi: The Euler-Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem. IMA Journal of Numerical Analysis, 41(2):1164-1196, 2021
P. Przybyłowicz, M. Szölgyenyi, F. Xu: Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps. Statistics and Probability Letters, 174(109072), 2021
P. Przybyłowicz, M. Szölgyenyi: Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift. Applied Mathematics and Computation, 403C(126191), 2021
S. Kremsner, A. Steinicke, M. Szölgyenyi: A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics. Risks - Special Issue "Computational Finance and Risk Analysis in Insurance", 8(4):136, 2020
K. Colaneri, Z. Eksi, R. Frey, M. Szölgyenyi: Optimal liquidation under partial information with price impact. Stochastic Processes and their Applications, 130(4):1913-1946, 2020
A. Neuenkirch, M. Szölgyenyi, L. Szpruch: An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. SIAM Journal on Numerical Analysis, 57(1):378-403, 2019
P. Kritzer, G. Leobacher, M. Szölgyenyi, S. Thonhauser: Approximation methods for piecewise deterministic Markov processes and their costs. Scandinavian Actuarial Journal, 2019(4):308-335, 2019
G. Leobacher, M. Szölgyenyi: Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient. Numerische Mathematik, 138(1):219-239, 2018
A. Eichler, G. Leobacher, M. Szölgyenyi: Utility indifference pricing of insurance catastrophe derivatives. European Actuarial Journal, 7:515-534, 2017
G. Leobacher, M. Szölgyenyi: A strong order 1/2 method for multidimensional SDEs with discontinuous drift. The Annals of Applied Probability, 27(4):2383-2418, 2017
A. A. Shardin, M. Szölgyenyi: Optimal control of an energy storage facility under a changing economic environment and partial information. International Journal of Theoretical and Applied Finance, 19(4):1-27, 2016
M. Szölgyenyi: Dividend maximization in a hidden Markov switching model. Statistics & Risk Modeling, 32(3-4):143-158, 2016
G. Leobacher, M. Szölgyenyi: A numerical method for SDEs with discontinuous drift. BIT Numerical Mathematics, 56(1):151-162, 2016
G. Leobacher, M. Szölgyenyi, S. Thonhauser: On the existence of solutions of a class of SDEs with discontinuous drift and singular diffusion. Electronic Communications in Probability, 20(6):1-14, 2015
G. Leobacher, M. Szölgyenyi, S. Thonhauser: Bayesian dividend optimization and finite time ruin probabilities. Stochastic Models, 30(2):216-249, 2014
M. Szölgyenyi: Bayesian dividend maximization: a jump diffusion model. In Vanmaele, M., Deelstra, G., De Schepper, A., Dhaene, J., Schoutens, W., Vanduffel, S., Vyncke, D. (Eds.): Handelingen Contactforum Actuarial and Financial Mathematics Conference, Interplay between Finance and Insurance, February 7-8, 2013, Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten, Brussel, 2013, ISBN 9789065691231
G. Larcher, L. Del Chicca, M. Szölgyenyi: Modeling and performance of certain put-write strategies. The Journal of Alternative Investments, 15(4):74-86. 2013
Invited Publications
M. Szölgyenyi: Stochastic differential equations with irregular coefficients: mind the gap! Internationale Mathematische Nachrichten, 246:43-56, 2021
G. Leobacher, M. Szölgyenyi: Numerical methods for SDEs with drift discontinuous on a set of positive reach. Internationale Mathematische Nachrichten, 235:1-16, 2017
Theses
M. Szölgyenyi: Optimal control of an energy storage facility in a hidden Markov model. Master’s Thesis (Economics), Johannes Kepler University Linz, 2015
M. Szölgyenyi: Dividend maximization in hidden Markov models and analysis of associated stochastic differential equations. PhD Thesis, Johannes Kepler University Linz, 2015
M. Szölgyenyi: Performance analysis of certain put-write strategies with different methods. Master’s Thesis (Mathematics), Johannes Kepler University Linz, 2011
