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

1982

### 55.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b$$^{1}$$$$\Sigma$$$$^{+}$$ and a$$^{1}$$$$\Delta$$ emissions from group VI-VI diatomic molecules: b0$$^{+}$$ → X$$_{1}$$0$$^{+}$$, X$$_{2}$$1 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

### 54.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b$$^{1}$$$$\Sigma$$$$^{+}$$ and a$$^{1}$$$$\Delta$$ emissions from group VI-VI diatomic molecules b0$$_{g}$$$$^{+}$$ → X$$^{2}$$1$$_{g}$$ emissions of Se$$_{2}$$ and Te$$_{2}$$
Chemical Physics Letters, 86 (2) :118-122
1982

### 53.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b$$^{1}$$$$\Sigma$$$$^{+}$$ and a$$^{1}$$$$\Delta$$ emissions from group VI-VI diatomic molecules b0$$_{g}$$$$^{+}$$ → X$$^{2}$$1$$_{g}$$ emissions of Se$$_{2}$$ and Te$$_{2}$$
Chemical Physics Letters, 86 (2) :118-122
1982

### 52.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C2O radicals in the C3O2 + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

### 51.

Becker, Karl Heinz; Horie, O.; Schmidt, V. H.; Wiesen, Peter
Spectroscopic identification of C$$_{2}$$O radicals in the C$$_{3}$$O$$_{2}$$ + O flame system by laser-induced fluorescence
Chemical Physics Letters, 90 (1) :64-68
1982

### 50.

Jensen, Per; Brodersen, Svend
The $$\nu$$$$_{5}$$ Raman band of CH$$_{3}$$CD$$_{3}$$
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

### 49.

Jensen, Per; Brodersen, Svend
The $$\nu$$$$_{5}$$ Raman band of CH$$_{3}$$CD$$_{3}$$
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

### 48.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH$$_{2}$$ in the X\verb=~=$$^{3}$$B$$_{1}$$ ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

### 47.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH$$_{2}$$ in the X\verb=~=$$^{3}$$B$$_{1}$$ ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

### 46.

Jensen, Per; Bunker, Philip R.; Hoy, A. R.
The equilibrium geometry, potential function, and rotation?vibration energies of CH2 in the X~3B1 ground state
The Journal of Chemical Physics, 77 (11) :5370-5374
1982

### 45.

Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982

### 44.

Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982

### 43.

Jensen, Per; Bunker, Philip R.
The geometry and the inversion potential function of formaldehyde in the and electronic states
Journal of Molecular Spectroscopy, 94 (1) :114-125
1982

### 42.

Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A\verb=~=$$^{1}$$A$$_{2}$$ and a\verb=~=$$^{3}$$A$$_{2}$$ electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
1982

### 41.

Jensen, Per; Bunker, Philip R.
The geometry and the out-of-plane bending potential function of thioformaldehyde in the A~1A2 and a~3A2 electronic states
Journal of Molecular Spectroscopy, 95 (1) :92-100
1982

### 40.

Jensen, Per; Brodersen, Svend
The ν5 Raman band of CH3CD3
Journal of Raman Spectroscopy, 12 (3) :295-299
1982

### 39.

Tausch, Michael W.; J. Plath, P.
Umlagerungen in (CH)₇⁺-Carbokationen
Revue Roumaine de Chimie, 27 :953
1982
1981

### 38.

Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO$$_{2}$$NO$$_{2}$$
Chemical Physics Letters, 83 (3) :459-464
1981

### 37.

Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO$$_{2}$$NO$$_{2}$$
Chemical Physics Letters, 83 (3) :459-464
1981

### 36.

Barnes, Ian; Bastian, V.; Becker, Karl Heinz; Fink, Ewald H.; Zabel, Friedhelm
Rate constant of the reaction of OH with HO2NO2
Chemical Physics Letters, 83 (3) :459-464
1981

### 35.

Tausch, Michael W.
THEORETISCHE UND EXPERIMENTELLE UNTERSUCHUNGEN VON VALENZISOMERISIERUNGEN
Herausgeber: Minerva Publikation, München
1981

### 34.

Tausch, Michael W.
Vorschlag für den Aufbau und die Bewertung einer Klausur zum Kurs ''Grundreaktionen in der organischen Chemie"
Praxis der Naturwissenschaften (Chemie), 30 :374
1981

### 33.

Jensen, Per; Brodersen, Svend; Guelachvili, Guy
Determination of A0 for CH335Cl and CH337Cl from the ν4 infrared and Raman bands
Journal of Molecular Spectroscopy, 88 (2) :378-393
1981

### 32.

Tausch, Michael W.
BINDUNG UND STRUKTUR - Unterrichtsbuch für die gymnasiale Oberstufe
Determination of A$$_{0}$$ for CH$$_{3}$$$$^{35}$$Cl and CH$$_{3}$$$$^{37}$$Cl from the $$\nu$$$$_{4}$$ infrared and Raman bands