Fakultät für Mathematik und Naturwissenschaften

## 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

2022

### 5629.

Bohrmann-Linde, Claudia; Siehr, Ilona
CHEMIE Einführungsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
August 2022

ISBN: 9783661060019

### 5628.

[german] Monique, Meier; Zeller, Diana; Stinken-Rösner, Lisa
Interaktive Videoformate für den naturwissenschaftlichen Unterricht. Vom Rezipieren zum Interagieren
Unterricht Biologie, 475 :44-47
07 2022

### 5627.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Strom aus Bäckerhefe
Nachrichten aus der Chemie, 70 (7-8) :18-21
Juli 2022

### 5626.

[german] Zeller, Diana
Medialab – ein dreistufiges Modul zur Entwicklung digitalisierungsbezogener Kompetenzen im Studium des Chemie‐ und Sachunterrichtslehramts
CHEMKON, 29 (S1) :287-292
Juni 2022

### 5625.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Entwicklung eines lowcost Experiments für den Chemieunterricht am Beispiel der enzymatischen Brennstoffzelle mit Lactase
CHEMKON, 29 (S1) :233-238
Juni 2022

### 5624.

[english] Bohrmann-Linde, Claudia; Zeller, Diana; Meuter, Nico; Tausch, Michael W.
Teaching Photochemistry: Experimental Approaches and Digital Media
ChemPhotoChem, 6 (6) :1-11
Juni 2022

### 5623.

[german] Zeller, Diana; Meier, Monique
Videos interaktiv erweitern - Forschendes Lernen vielseitig unterstützen
Digital Unterricht Biologie, 4 :10-11
Mai 2022

### 5622.

[german] Gökkus, Yasemin; Tausch, Michael W.
Explorative Studie zur partizipativen und nutzenorientierten Forschung in der Chemiedidaktik
CHEMKON, 29 (3) :117-124
April 2022

### 5621.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 5620.

Gerlach, Moritz; Glück, Jochen
On characteristics of the range of integral operators
2022

### 5619.

Bolten, M.; De Sturler, E.; Hahn, C.
Krylov Subspace Recycling for Evolving Structures
Comput. Methods Appl. Mech. Engrg., 391 :114222
2022

### 5618.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal Optimization Through Multi-objective Reformulation
math.OC, arXiv:2204.02003
2022
Herausgeber: arXiv

### 5617.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

### 5616.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
2022

### 5615.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

### 5614.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective Matroid Optimization with Ordinal Weights
Discrete Applied Mathematics
2022

### 5613.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 5612.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

### 5611.

Daners, Daniel; Glück, Jochen; Mui, Jonathan
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
2022

### 5610.

[german] Tausch, Michael W.
LED statt Gasbrenner - Mehr Licht für nachhaltigen Chemieunterricht
Chemie in unserer Zeit, 56 (3/2022) :188–196
2022

### 5609.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

### 5608.

[german] Banerji, Amitabh; Dörschelln, Jennifer; Schwarz, D.
Organische Leuchtdioden im Chemieunterricht
Chemie in unserer Zeit, 52 (1) :34-41
2022

### 5607.

[german] Zeller, Diana; Bohrmann-Linde, Claudia
#debunk YouTube-Videos - Ein didaktisches Konzept zum Einsatz von Videos im Chemieunterricht zur Stärkung der Digital Scientific Literacy
MNU journal, 75 (03) :197-201
2022

### 5606.

Ballaschk, Frederic; Kirsch, Stefan F.
Oxidations with Iodine(V) Compounds – From Stoichiometric Compounds to Catalysts
In Ishihara, Kazuaki and Muñiz, Kilian, Editor, Iodine Catalysis in Organic Synthesis
Seite 299–334
Herausgeber: Wiley
1 Edition
2022
299–334

### 5605.

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

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