Advances in Mathematical Economics Volume 15 [electronic resource] /
Kusuoka, Shigeo.editor.
Maruyama, Toru.editor.
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.
Description based upon print version of record.
Advances inMathematical Economics; Table of Contents; Some various convergence results for normal integrands; 1 Introduction; 2 Notations and preliminaries; 3 Multivalued conditional expectation theorem; 4 Conditional expectation in a dual space; 5 On various convergence problems for normal integrands; References; A note on robust representations of law-invariant quasiconvex functions; 1 Introduction; 2 Notations, definitions and the Fatou property; 3 Representation results for law-invariant risk measures; 4 Time-consistent law-invariant quasiconcave functions; 5 Examples; References
On the Fourier analysis approach to the Hopf bifurcation theorem1 Introduction; 2 Abstract Hopf bifurcation theorem; 3 Classical Hopf bifurcation for ordinary differential equations; 4 Smoothness of F; 5 dimV=2; 6 codimR=2; 7 Linear independence of PMv* and PNv* (I); 8 Linear independence of PMv* and PNv* (II); 9 Hopf bifurcation in Cr; References; Fixed point theorems and ergodic theorems for nonlinear mappings in Banach spaces; 1 Introduction; 2 Preliminaries; 3 Fixed point theorems; 4 Some properties of generalized nonspreading mappings; 5 Nonlinear ergodic theorems
6 Weak convergence theoremsReferences; On the perception and representation of economic quantity in the history of economic analysis in view of the Debreu conjecture; 1 Introduction; 1.1 The Debreu conjecture; 1.2 The related theoretical framework; 1.3 The perception of economic quantity; 2 The perception and representation of economic quantity in selected literature of economic analysis; 2.1 Perception and representation of economic quantity in Cournot's theory; 2.2 Perception and representation of economic quantity in Walras; 2.3 Perception and representation of economic quantity in Pareto
2.4 Perception and representation of economic quantity in Marshall3 The perceptions of Cournot, Walras, Pareto, and Marshall in relation to the literature of the 1950sand 1960s; 3.1 Property of economic variables: perception as quantities or functions; 3.2 Common perception on the continuity of market demand; 4 The perception of economic quantity in the history of economic analysis and the Debreu conjecture; 4.1 The interpretation of perceptions of ``discontinuity'' in modern economic analysis
4.2 The Debreu conjecture and the interpretation of the common perception of the continuity of market demandsReferences; An existence result and a characterization of the least concave utility of homothetic preferences; 1 Introduction; 2 The main result; 3 Proof; References; Subject Index; Instructions for Authors
Includes bibliographical references and index.
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.
Economic theory.
Game theory.
Economic Theory/Quantitative Economics/Mathematical Methods.
Game Theory, Economics, Social and Behav. Sciences.

Advances in Mathematical Economics