Bernd Luderer

On necessary minimum conditions in quasidifferential calculus: independence of the specific choice of quasidifferentials

Various necessary minimum conditions in quasidifferential calculus are compared. These conditions as well as regularity conditions and some estimates of directional derivatives are studied concerning their dependence on the special choice of a quasidifferential. Moreover, a generalized notion of quasidifferentiability for functions possibly having infinite directional derivatives is introduced.

Directional derivative estimates for the optimal value function of a quasidifferentiable programming problem

This paper is concerned with the optimal value function arising in the primal decomposition of a quasidifferentiable programming problem. In particular, estimates for the upper Dini directional derivative of this function are derived. They involve certain “Lagrange multipliers” occurring in the necessary minimum conditions to the lower level problems. This study generalizes some previously published results on this subject.

On Shapiro's results in quasidifferential calculus

Several necessary minimum conditions for quasidifferentiable programming problems are discussed. Some statements of Shapiro (1986) are shown to be incorrect.

Multivalued analysis and nonlinear programming problems with perturbations

Preface. 1. Basic Notation. 2. Basic Problems of Multivalued Analysis. 3. Properties of Multivalued Mappings. 4. Subdifferentials of Marginal Functions. 5. Derivatives of Marginal Functions. 6. Sensitivity Analysis. Bibliographical Comments. References. Index.

Calculus of Probability

A trial is an attempt (observation, experiment) the result of which is uncertain within the scope of some possibilities and which is, at least in ideas, arbitrarily often reproducible when remaining unchanged the external conditions characterizing the attempt.

Does the Special Choice of Quasidifferentials Influence Necessary Minimum Conditions

In dealing with nonsmooth functions quasidifferential calculus is an important means. Created about ten years ago /2/, this theory is well elaborate at present (see /1/, /3/, /4/). In the present paper we are mainly concerned with necessary minimum conditions and study the question whether the specific choice of quasidifferentials, which can be taken from a whole equivalence class, influences the sets of stationary points, the validity of constraint qualifications or some bounds for directional derivatives of marginal functions.

Mathe, Märkte und Millionen. Faire Preise und Marktpreise

Was versteht man unter dem „fairen“ Preis eines Finanzprodukts und in welchem Verhaltnis steht dieser zum tatsachlich am Markt gehandelten Preis?

Algorithms of Quasidifferentiable Optimization for the Separation of Point Sets

An algorithm for finding the intersection of the convex hulls of two sets consisting of finitely many points each is proposed. The problem is modelled by means of a quasidifferentiable (in the sense of Demyanov and Rubinov) optimization problem, which is solved by a descent method for quasidifferentiable functions.

Differential Calculus for Functions of Several Variables

Functions y = f(x 1, x 2) of two independent variables x 1, x 2 can be visualized in a three-dimensional representation by a (x 1, x 2, y)-system of co-ordinates. The set of points (x 1, x 2, y) forms a surface provided that the function f is continuous. The set of points (x 1, x 2) such that f(x 1, x 2) = C = const is called a height line or level line of the function f to the height (level) C. These lines are located in the x 1, x 2-plane.

Bewertung und Hedging von Swaptions

Zinsswaps (Interest Rate Swaps, IRS) (vgl. Biermann, 2002, S. 135 ff.; Hull, 2000, S. 121 ff.; Luderer/Zuchanke, 2000) werden seit längerer Zeit von Großunternehmen zum Hedgen gegen Zinsänderungsrisiken eingesetzt. Ein Kreditnehmer, der einen Zinsanstieg erwartet, kann mit einem Swap seine variable in eine feste Zinsverpflichtung umwandeln. Dadurch ist er in der Lage, für ihn ungünstige Einflüsse von Zinsschwankungen in Grenzen zu halten.