Applied and Computational Mathematics (ACM)

Finance

The famous Black-Scholes equation is an effective model for option pricing. It was named after the pioneers Black, Scholes and Merton who suggested it 1973.

In this research field our aim is the development of effective numerical schemes for solving linear and nonlinear problems arising in the mathematical theory of derivative pricing models.

An option is the right (not the duty) to buy (`call option') or to sell (`put option') an asset (typically a stock or a parcel of shares of a company) for a price E by the expiry date T. European options can only be exercised at the expiration date T. For American options exercise is permitted at any time until the expiry date. The standard approach for the scalar Black-Scholes equation for European (American) options results after a standard transformation in a diffusion equation posed on an bounded (unbounded) domain.

Another problem arises when considering American options (most of the options on stocks are American style). Then one has to compute numerically the solution on a semi-unbounded domain with a free boundary. Usually finite differences or finite elements are used to discretize the equation and artificial boundary conditions are introduced in order to confine the computational domain.

In this research field we want to design and analyze new efficient and robust numerical methods for the solution of highly nonlinear option pricing problems. Doing so, we have to solve adequately the problem of unbounded spatial domains by introducing artificial boundary conditions and show how to incorporate them in a high-order time splitting method.

Nonlinear Black-Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values than the classical linear model by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor's preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option price itself.



Special Interests

Publications



2024

5275.

[german] Zeller, Diana; Bohrmann-Linde, Claudia; Mack, Nils; Diekmann, Charlotte; Schrader, Claudia
Virtual Reality für den Chemieunterricht
Nachrichten aus der Chemie, 72 (6) :15-22
2024

5274.

Acu, Ana-Maria; Heilmann, Margareta; Raş, Ioan; Steopoaie, Ancuta Emilia
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov operators
Applicable Analysis and Discrete Mathematics :1-16
2024

5273.


Sprachsensibler Chemieunterricht digital umgesetzt - Ein Seminarexkurs im Rahmen des Praxissemesters
2024

5272.

Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences

5271.

Bartel, Andreas; Diab, Malak; Frommer, Andreas; Günther, Michael; Marheineke, Nicole
Splitting Techniques for DAEs with port-Hamiltonian Applications
Preprint
2024

5270.

Bartel, Andreas; Clemens, Markus; Günther, Michael; Jacob, Birgit; Reis, Timo
Port-Hamiltonian systems’ modelling in electrical engineering
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor, Scientific Computing in Electrical Engineering: SCEE 2022, Amsterdam, The Netherlands, July 2022ausMathematics in Industry, Seite 133–143
In van Beurden, Martijn and Budko, Neil V. and Ciuprina, Gabriela and Schilders, Wil and Bansal, Harshit and Barbulescu, Ruxandra, Editor
Herausgeber: Springer Cham
2024

5269.

Jacob, Birgit; Glück, Jochen; Meyer, Annika; Wyss, Christian; Zwart, Hans
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
J. Evol. Equ., 24 :Paper No. 62
2024

5268.

Bartel, A.; Clemens, M.; Günther, M.; Jacob, Birgit; Reis, T.
Port-Hamiltonian Systems Modelling in Electrical Engineering
Band 43
Herausgeber: Springer, Cham.
van Beurden, M., Budko, N.V., Ciuprina, G., Schilders, W., Bansal, H., Barbulescu, R. Edition
2024

5267.

Fasi, Massimiliano; Gaudreault, Stéphane; Lund, Kathryn; Schweitzer, Marcel
Challenges in computing matrix functions
2024

5266.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and xj
Mathematical Methods in the Applied Sciences, 47 (18) :13718-13733
2024

5265.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators
2024

5264.

Bauß, Julius; Stiglmayr, Michael
Augmenting Biobjective Branch & Bound with Scalarization-Based Information
Mathematical Methods of Operations Research
2024

5263.

Vinod, Vivin; Zaspel, Peter
Benchmarking Data Efficiency in Δ-ML and Multifidelity Models for Quantum Chemistry.
2024

5262.

Kiesling, Elisabeth; Venzlaff, Julian; Bohrmann-Linde, Claudia
BNE-Fortbildungsreihe für Lehrkräfte und Studierende in der Didaktik der Chemie
Herausgeber: Gemeinsamer Studienausschuss (GSA) in der School of Education an der Bergischen Universität Wuppertal
Newsletter Lehrer*innenbildung an der Bergischen Universität Wuppertal
Juli 2024

5261.

Klass, Friedemann; Bartel, Andreas; Gabbana, PD Alessandro
Boundary conditions for multi-speed lattice Boltzmann methods
2024

5260.

Bailo, Rafael; Barbaro, Alethea; Gomes, Susana N.; Riedl, Konstantin; Roith, Tim; Totzeck, Claudia; Vaes, Urbain
CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods
Journal of Open Source Software, 9 (98) :6611
2024
Herausgeber: The Open Journal

5259.

Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195–208
2024
Herausgeber: Pergamon

5258.

Bauß, Julius; Stiglmayr, Michael
Adapting Branching and Queuing for Multi-objective Branch and Bound
Operations Research Proceedings 2023
Herausgeber: Springer
2024

5257.

Klass, Friedemann; Gabbana, Alessandro; Bartel, Andreas
Characteristic boundary condition for thermal lattice Boltzmann methods
Computers & Mathematics with Applications, 157 :195-208
Juli 2024
ISSN: 0898-1221

5256.

Yoda, R.; Bolten, M.; Nakajima, K.; Fujii, A.
Coarse-grid operator optimization in multigrid reduction in time for time-dependent Stokes and Oseen problems
Jpn. J. Ind. Appl. Math.
2024

5255.

Abel, Ulrich; Acu, Ana Maria; Heilmann, Margareta; Raşa, Ioan
Commutativity and spectral properties for a general class of Szasz-Mirakjan-Durrmeyer operators
Advances in Operator Theory, 10 (1) :14
2024

5254.

Vorberg, Lukas; Jacob, Birgit; Wyss, Christian
Computing the Quadratic Numerical Range
Journal of Computational and Applied Mathematics :116049
2024

5253.

Klamroth, Kathrin; Stiglmayr, Michael; Totzeck, Claudia
Consensus-Based Optimization for Multi-Objective Problems: A Multi-Swarm Approach
Journal of Global Optimization
2024

5252.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London

5251.

Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London