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



2023

5125.

Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv

5124.

Wintermayr, Jens; Kerner, Joachim; Täufer, Matthias
Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice
Annales Henri Poincare :19
Dezember 2023

5123.

Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon

5122.

Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
2023

5121.

Clemens, Markus; Günther, Michael
Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework
2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), Seite 1–1
Herausgeber: IEEE
2023

5120.


Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters A :128611
2023
Herausgeber: North-Holland

5119.

Guerreiro, Andreia P.; Klamroth, Kathrin; Fonseca, Carlos M.
Theoretical aspects of subset selection in multi-objective optimization
In Brockhoff, D. and Emmerich, M. and Naujoks, B. and Purshouse, R., Editor aus Natural Computing Series
Seite 213--239
Herausgeber: Springer
2023
213--239

5118.

[english] Rendon-Enriquez, Ibeth; Palma-Cando, Alex; Körber, Florian; Niebisch, Felix; Forster, Michael; Tausch, Michael W.; Scherf, Ullrich
Thin Polymer Films by Oxidative or Reductive Electropolymerization and Their Application in Electrochromic Windows and Thin-Film Sensors
molecules, 28 (2) :883
Januar 2023

5117.

Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI

5116.

Ehrhardt, Matthias
Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction
Journal of Marine Science and Engineering, 11 (10) :1922
2023
Herausgeber: MDPI

5115.

Bülow, Friedrich; Hahn, Yannik; Meyes, Richard; Meisen, Tobias; others
Transparent and Interpretable State of Health Forecasting of Lithium-Ion Batteries with Deep Learning and Saliency Maps
International Journal of Energy Research, 2023
2023
Herausgeber: Hindawi

5114.

Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland

5113.

Ehrhardt, Matthias
Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons
Physics Letters, Section A, 459 :128611
2023
Herausgeber: North-Holland

5112.

David, Amelie; Stroka, Steven; Haussmann, Norman; Schmülling, Benedikt; Clemens, Markus
Überprüfung der elektromagnetischen Umweltverträglichkeit bei induktiver Ladung
In Proff, Heike and Clemens, Markus and Marrón, Pedro J. and Schmülling, Benedikt, Editor
Seite 143-180
Herausgeber: Springer Fachmedien Wiesbaden, Wiesbaden
2023
143-180

5111.

Meinert, Janning; Morej\'on, Leonel; Sandrock, Alexander; Eichmann, Björn; Kreidelmeyer, Jonas; Kampert, Karl-Heinz
The impact of a modified CMB photon density on UHECR propagation
PoS, ICRC2023 :322
2023

5110.

Dobrick, Alexander; Hölz, Julian; Kunze, Markus
Ultra Feller operators from a functional analytic perspective
2023

5109.

Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Submitted to SIAM-ASA J. Uncertain. Quantif.
2023

5108.

Kapllani, Lorenc; Teng, Long; Rottmann, Matthias
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
2023

5107.

Dobrick, Alexander; Hölz, Julian
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
2023

5106.

Abdul Halim, Adila; others
Update on the Offline Framework for AugerPrime and production of reference simulation libraries using the VO Auger grid resources
PoS, ICRC2023 :248
2023

5105.

Ehrhardt, Matthias
Use of interference patterns to control sound field focusing in shallow water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI

5104.

Ehrhardt, Matthias
Use of Interference Patterns to Control Sound Field Focusing in Shallow Water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI

5103.

Jendoubi, Oussama
Vergleich der magnetischen Streufeldwerte eines induktiven geladenen Taxis zwischen Simulation und Messung im Rahmen des TALAKO-Projekts
2023

5102.

Alameddine, Jean-Marco; others
The particle-shower simulation code CORSIKA 8
PoS, ICRC2023 :310
2023

5101.

Lund, Kathryn; Schweitzer, Marcel
The Frechet derivative of the tensor t-function
Calcolo, 60
2023