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

1983

### 80.

Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
Mechanisms of perhydroxyl HO$$_{2}$$(A$$^{2}$$A') excitation in various chemical systems
The Journal of Physical Chemistry, 87 (20) :3943-3948
1983

### 79.

Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=$$^{3}$$B$$_{1}$$ electronic state of methylene CH$$_{2}$$
The Journal of Chemical Physics, 79 (3) :1224-1228
1983

### 78.

Bunker, Philip R.; Jensen, Per
A refined potential surface for the X\verb=~=$$^{3}$$B$$_{1}$$ electronic state of methylene CH$$_{2}$$
The Journal of Chemical Physics, 79 (3) :1224-1228
1983

### 77.

Bunker, Philip R.; Jensen, Per
A refined potential surface for the X~3B1 electronic state of methylene CH2
The Journal of Chemical Physics, 79 (3) :1224-1228
1983

### 76.

Winter, R.; 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 TeSe
Chemical Physics Letters, 94 (3) :335-338
1983

### 75.

Winter, R.; 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 TeSe
Chemical Physics Letters, 94 (3) :335-338
1983

### 74.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b$$^{1}$$$$\Sigma$$$$^{+}$$ Emissions from group V-VII diatomic molecules: b0$$^{+}$$ → X$$_{1}$$0$$^{+}$$ emission of Pl
Chemical Physics Letters, 102 (5) :404-408
1983

### 73.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, J{ü}rgen
b$$^{1}$$$$\Sigma$$$$^{+}$$ Emissions from group V-VII diatomic molecules: b0$$^{+}$$ → X$$_{1}$$0$$^{+}$$ emission of Pl
Chemical Physics Letters, 102 (5) :404-408
1983

### 72.

Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeSe
Chemical Physics Letters, 94 (3) :335-338
1983

### 71.

Winter, R.; Kruse, H.; Fink, Ewald H.; Wildt, Jürgen
b1Σ+ Emissions from group V-VII diatomic molecules: b0+ → X10+ emission of Pl
Chemical Physics Letters, 102 (5) :404-408
1983

### 70.

Tausch, Michael W.
Chemische Solarenergiespeicherung in Valenzisomeren
Praxis der Naturwissenschaften (Chemie), 32 :79
1983

### 69.

Tausch, Michael W.
DER UV-TAUCHLAMPENREAKTOR FÜR PHOTOCHEMISCHE SCHULVERSUCHE, Monographie mit Versuchsanleitungen und didaktischen Hinweisen
Herausgeber: SCS Jürgens\&Co KG, Bremen
1983

### 68.

Jensen, Per
HCNO as a semirigid bender: The degenerate $$\nu$$$$_{4}$$ state
Journal of Molecular Spectroscopy, 101 (2) :422-439
1983

### 67.

Jensen, Per
HCNO as a semirigid bender: The degenerate $$\nu$$$$_{4}$$ state
Journal of Molecular Spectroscopy, 101 (2) :422-439
1983

### 66.

Jensen, Per
HCNO as a semirigid bender: The degenerate ν4 state
Journal of Molecular Spectroscopy, 101 (2) :422-439
1983

### 65.

Holstein, K. J.; Fink, Ewald H.; Wildt, J{ü}rgen; Winter, R.; Zabel, Friedhelm
Mechanisms of perhydroxyl HO$$_{2}$$(A$$^{2}$$A') excitation in various chemical systems
The Journal of Physical Chemistry, 87 (20) :3943-3948
1983
1982

### 64.

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

### 63.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b$$^{1}$$$$\Sigma$$$$^{+}$$ emissions from group V-VII diatomic molecules: b0$$^{+}$$ → X$$_{1}$$0$$^{+}$$, X$$_{2}$$0$$^{+}$$ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

### 62.

Tausch, Michael W.
Modelle im Chemieunterricht
Der mathematische und naturwissenschaftliche Unterricht (MNU), 35 :226
1982

### 61.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ emissions from group V-VII diatomic molecules: b0+ → X10+, X20+ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

### 60.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules: b0+ → X10+, X21 emissions of TeO and TeS
Journal of Molecular Structure, 80 :75-82
1982

### 59.

Winter, R.; Barnes, Ian; Fink, Ewald H.; Wildt, Jürgen; Zabel, Friedhelm
b1Σ+ and a1Δ emissions from group VI-VI diatomic molecules b0g+ → X21g emissions of Se2 and Te2
Chemical Physics Letters, 86 (2) :118-122
1982

### 58.

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

### 57.

Kruse, H.; Winter, R.; Fink, Ewald H.; Wildt, J{ü}rgen; Zabel, Friedhelm
b$$^{1}$$$$\Sigma$$$$^{+}$$ emissions from group V-VII diatomic molecules: b0$$^{+}$$ → X$$_{1}$$0$$^{+}$$, X$$_{2}$$0$$^{+}$$ emissions of SbBr
Chemical Physics Letters, 93 (5) :475-479
1982

### 56.

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

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