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

2023

6818.

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

6817.

Pereselkov, Sergey; Kuz’kin, Venedikt; Ehrhardt, Matthias; Tkachenko, Sergey; Rybyanets, Pavel; Ladykin, Nikolay
Use of Interference Patterns to Control Sound Field Focusing in Shallow Water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI

6816.

Pereselkov, Sergey; Kuz’kin, Venedikt; Ehrhardt, Matthias; Tkachenko, Sergey; Rybyanets, Pavel; Ladykin, Nikolay
Use of Interference Patterns to Control Sound Field Focusing in Shallow Water
Journal of Marine Science and Engineering, 11 (3) :559
2023
Herausgeber: MDPI

6815.

Abel, Ulrich; Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Voronovskaja formula for Aldaz-Kounchev-Render operators: uniform convergence
submitted
2023

6814.

Acu, A.M.; Heilmann, Margareta; Raşa, I.; Steopoaie, Ancuta Emilia
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov Operators
submitted
2023

6813.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Voronovskaja type results for the Aldaz-Kounchev-Render versions of generalized Baskakov Operators
submitted

6812.

Jacob, Birgit; Günther, Michael; Ehrhardt, Matthias
Analysis and Numerics of port-Hamiltonian systems Schedule (Start of Seminar: Oct 26, 2022)

6811.

Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

6810.

Ehrhardt, M
Asymptotische Analysis Vorlesungszeiten

6809.

Ehrhardt, Matthias
Computerunterstützte Mathematik Zeiten

6808.

Acu, A.M.; Heilmann, Margareta; Raşa, I.
Bulleting of the Malaysian Math. Sciences Society

6807.

Tripiccione, Betreuer Raffaele; Ehrhardt, Matthias; Alexandrou, Constantia; Toschi, Federico; Simma, Hubert; Schifano, Co-Betreuer Sebastiano Fabio
Daniele Simeoni 1836010

6806.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6805.

Ehrhardt, Matthias
Ein einfaches Kompartment-Modell zur Beschreibung von Revolutionen am Beispiel des Arabischen Frühlings

6804.

Günther, Michael
Einführung in die Finanzmathematik

6803.

Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital

6802.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6801.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6800.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

6799.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

6798.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

6797.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; V{\'a}zquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89

6796.

Carmen Calvo-Garrido, Mar{\i}a; Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89

6795.

Putek, PA; Ter Maten, EJW; Günther, M
Reliability-based Low Torque Ripple Design of Permanent Magnet Machine

6794.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

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