## Fachbereich Mathematik

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- 1999 (129) (remove)

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#### Keywords

- Numerical solution of a nonstandard Darcy flow model (1999)
- We consider a Darcy flow model with saturation-pressure relation extended with a dynamic term, namely, the time derivative of the saturation. This model was proposed in works of J.Hulshof and J.R.King (1998), S.M.Hassanizadeh and W.G.Gray (1993), F.Stauffer (1978). We restrict ourself to one spatial dimension and strictly positive initial saturation. For this case we transform the initial-boundary value problem into combination of elliptic boundary-value problem and initial value problem for abstract Ordinary Differential Equation. This splitting is rather helpful both for theoretical aspects and numerical methods.

- Spektralsequenzen (1999)
- Das Lehrskript "Spektralsequenzen" fuehrt die Begriffe der exakten und abgeleiteten Paare sowie der Spektralsequenzen in der Kategorie der m-graduierten Moduln ein. Naeher betrachtet werden die Begriffe dann fuer Doppelkomplexe mit Filtrationen.

- Monodromie von Differentialgleichungen (1999)
- Einführung und Grundlagen. SS 1996 und WS 1996/7.

- Computation of the Monodromy of an Isolated Hypersurface Singularity (1999)
- This thesis deals with the implementation of an algorithm to compute the monodromy of an isolated hypersurface singularity in the computer algebra system Singular.

- Some Applications of Impulse Control in Mathematical Finance (1999)
- We consider three applications of impulse control in financial mathematics, a cash management problem, optimal control of an exchange rate, and portfolio optimisation under transaction costs. We sketch the different ways of solving these problems with the help of quasi-variational inequalities. Further, some viscosity solution results are presented.

- Hyperplane transversals of homothetical, centrally symmetric polytopes (1999)
- Let P c R^n, n >= 2, be a centrally symmetric, convex n-polytope with 2r vertices, and P be a family of m >= n + 1 homothetical copies of P. We show that a hyperplane transversal of all members of P (it it exists) can be found in O(rm) time.

- A Fuzzy Programming Approach to Multicriteria Facility Location Problems (1999)
- Facility Location Problems are concerned with the optimal location of one or several new facilities, with respect to a set of existing ones. The objectives involve the distance between new and existing facilities, usually a weighted sum or weighted maximum. Since the various stakeholders (decision makers) will have different opinions of the importance of the existing facilities, a multicriteria problem with several sets of weights, and thus several objectives, arises. In our approach, we assume the decision makers to make only fuzzy comparisons of the different existing facilities. A geometric mean method is used to obtain the fuzzy weights for each facility and each decision maker. The resulting multicriteria facility location problem is solved using fuzzy techniques again. We prove that the final compromise solution is weakly Pareto optimal and Pareto optimal, if it is unique, or under certain assumptions on the estimates of the Nadir point. A numerical example is considered to illustrate the methodology.

- Multicriteria Ordered Weber Problems (1999)
- In this paper we deal with the determination of the whole set of Pareto-solutions of location problems with respect to Q general criteria.These criteria include median, center or cent-dian objective functions as particular instances.The paper characterizes the set of Pareto-solutions of a these multicriteria problems. An efficient algorithm for the planar case is developed and its complexity is established. Extensions to higher dimensions as well as to the non-convexcase are also considered.The proposed approach is more general than the previously published approaches to multi-criteria location problems and includes almost all of them as particular instances.

- On value preserving and growth optimal portfolios (1999)
- In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets.

- Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios (1999)
- We present some new general results on the existence and form of value preserving portfolio strategies in a general semimartingale setting. The concept of value preservation will be derived via a mean-variance argument. It will also be embedded into a framework for local approaches to the problem of portfolio optimisation.