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61.
62.
Igor V. Evstigneev Thorsten Hens Klaus Reiner Schenk-Hopp�� 《Mathematics and Financial Economics》2011,5(3):185-202
This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study
of local stability of the wealth dynamics through the application of recent results on the linearization and stability of
random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample
paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary
stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived,
extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial
dynamic models involving randomness. 相似文献
63.
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In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported. 相似文献
65.
Reiner Ansorge 《Applications of Mathematics》2003,48(6):417-427
Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations in a trivial way. It is a concern of this article to extend the theory in such a way that inequalities can be replaced by general relations, and this not only in an abstract way but also realized by examples. 相似文献
66.
Global optimization of concave functions subject to quadratic constraints: An application in nonlinear bilevel programming 总被引:2,自引:0,他引:2
When the follower's optimality conditions are both necessary and sufficient, the nonlinear bilevel program can be solved as a global optimization problem. The complementary slackness condition is usually the complicating constraint in such problems. We show how this constraint can be replaced by an equivalent system of convex and separable quadratic constraints. In this paper, we propose different methods for finding the global minimum of a concave function subject to quadratic separable constraints. The first method is of the branch and bound type, and is based on rectangular partitions to obtain upper and lower bounds. Convergence of the proposed algorithm is also proved. For computational purposes, different procedures that accelerate the convergence of the proposed algorithm are analysed. The second method is based on piecewise linear approximations of the constraint functions. When the constraints are convex, the problem is reduced to global concave minimization subject to linear constraints. In the case of non-convex constraints, we use zero-one integer variables to linearize the constraints. The number of integer variables depends only on the concave parts of the constraint functions.Parts of the present paper were prepared while the second author was visiting Georgia Tech and the University of Florida. 相似文献
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68.
Ohne Zusammenfassung
Joseph Hersch zum 70. Geburtstag gewidmet
Entstanden aus einem Aufenthalt des zweiten Autors am Forschungsinstitut für Mathematik an der ETH Zürich. 相似文献
69.
Reiner Kühnau 《Mathematische Annalen》1994,299(1):779-784
Ohne Zusammenfassung
Im Gedenken an Herbert Grötzsch (1902–1993) 相似文献
70.