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

1988

### 263.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

### 262.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a\(^{1}\)\(\Delta\)(a2)-X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{2}\)1) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

### 261.

Fink, Ewald H.; Setzer, Klaus-Dieter; Kottsieper, U.; Ramsay, D. A.; Vervloet, M.
The a1Δ(a2)-X3Σ-(X21) electronic band system of selenium monoxide
Journal of Molecular Spectroscopy, 131 (1) :127-132
1988

### 260.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

### 259.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X\verb=~=\(^{3}\)B\(_{1}\) methylene (CH\(_{2}\)) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

### 258.

Jensen, Per; Bunker, Philip R.
The potential surface and stretching frequencies X~3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian
The Journal of Chemical Physics, 89 (3) :1327-1332
1988

### 257.

[german] Tausch, Michael W.; Paterkiewicz, D.
Fluoreszenz und Phosphoreszenz
Praxis der Naturwissenschaften (Chemie), 36 :14
1988

### 256.

Weinmüller, E.; Winkler, E.
Path-following Algorithm for Singular Boundary Value Problems
ZAMM, 68 :527--537
1988

### 255.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

### 254.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

### 253.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

### 252.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

### 251.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC+ and C3 using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

### 250.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

### 249.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO\(_{3}\) and the Determination of Absolute Rate Constants for the Reaction of the NO\(_{3}\) Radical with CH\(_{3}\)SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

### 248.

Rahman, M. M.; Becker, Eilhard; Benter, Thorsten; Schindler, Ralph N.
A Gasphase Kinetic Investigation of the System F + HNO3 and the Determination of Absolute Rate Constants for the Reaction of the NO3 Radical with CH3SH, 2-Methylpropene, 1,3-Butadiene and 2,3-Dimethyl-2-Butene
Berichte der Bunsengesellschaft für physikalische Chemie, 92 (1) :91-100
1988

### 247.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

### 246.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

### 245.

Jensen, Per
A new morse oscillator-rigid bender internal dynamics (MORBID) Hamiltonian for triatomic molecules
Journal of Molecular Spectroscopy, 128 (2) :478-501
1988

### 244.

Jensen, Per; Kraemer, Wolfgang P.
A comparison of perturbative and variational rotation-vibration energies calculated for HOC\(^{+}\) and C\(_{3}\) using the nonrigid bender and MORBID Hamiltonians
Journal of Molecular Spectroscopy, 129 (1) :172-185
1988

### 243.

Jensen, Per; Kraemer, Wolfgang P.
A variational calculation of the rotation-vibration energies for CNC\(^{+}\) and CCN\(^{+}\)
Journal of Molecular Spectroscopy, 129 (1) :216-222
1988

### 242.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO\(_{3}\) radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

### 241.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO3 radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

### 240.

Benter, Thorsten; Schindler, Ralph N.
Absolute rate coefficients for the reaction of NO\(_{3}\) radicals with simple dienes
Chemical Physics Letters, 145 (1) :67-70
1988

### 239.

Jensen, Per
Calculation of rotation-vibration linestrengths for triatomic molecules using a variational approach
Journal of Molecular Spectroscopy, 132 (2) :429-457
1988

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