Kusuoka / Maruyama Advances in Mathematical Economics Volume 13

1. Auflage 2010
ISBN: 978-4-431-99490-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 208 Seiten

Advances in Mathematical Economics is a publication of the Research Center for Mathematical Economics, which was founded in 1997 as an international scientific association that aims to promote research activities in mathematical economics. Our publication was launched to realize our long-term goal of bringing together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research. The scope of Advances in Mathematical Economics includes, but is not limited to, the following fields: - economic theories in various fields based on rigorous mathematical reasoning; - mathematical methods (e.g., analysis, algebra, geometry, probability) motivated by economic theories; - mathematical results of potential relevance to economic theory; - historical study of mathematical economics. Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, we will also invite articles which might be considered too long for publication in journals.

Autoren/Hrsg.

Kusuoka, Shigeo

Maruyama, Toru

Inhaltsverzeichnis

1;Table of Contents;6
2;Some various convergence results for multivalued martingales;7
2.1;1 Introduction;7
2.2;2 Preliminaries and background;8
2.3;3 Convergence results for cwk(E)-valued martingales and mils;10
2.4;4 Convergences and conditional expectationin Pettis integration;19
2.5;5 Convergence of cwk(E)-valued Pettis-integrable martingales;32
2.6;References;37
3;A note on Aumann's core equivalence theorem without monotonicity;40
3.1;1 Introduction;40
3.2;2 The model;42
3.3;3 The core and quasi-equilibrium allocations;43
3.4;4 Irreducible economies;44
3.5;5 Conclusion;50
3.6;References;51
4;On two classical turnpike results for the Robinson–Solow–Srinivasan model;52
4.1;1 Introduction;53
4.2;2 The model and antecedent results;60
4.3;3 The principal results;68
4.4;4 The heuristics of the proofs;74
4.5;5 Concluding observations;77
4.6;6 Six auxiliary propositions;78
4.7;7 Four substantive lemmata;83
4.8;8 Proofs: proof of Theorem A;94
4.9;9 Proofs: proof of Theorem B;97
4.10;References;100
5;A certain limit of iterated conditional tail expectation;103
5.1;1 Introduction;103
5.2;2 Associated nonlinear PDE;106
5.3;3 Proof of main results;109
5.4;References;114
6;Set-valued optimization in welfare economics;116
6.1;1 Introduction;117
6.2;2 Tools of variational analysis and generalized differentiation;120
6.3;3 Solution notions and necessary optimality conditions in constrained multiobjective optimization;124
6.4;4 Local versions of the second welfare theorem;133
6.5;5 Global versions of the second welfare theorem;148
6.6;References;154
7;Convexity of the lower partition range of a concave vector measure;157
7.1;1 Introduction;157
7.2;2 Convex combinations of measurable sets;158
7.3;3 Convex structure of concave measures;160
7.4;4 An application to the fair division problem;161
7.5;References;162
8;Good locally maximal programs for the Robinson–Solow–Srinivasan model;163
8.1;1 Introduction;163
8.2;2 Main results;168
8.3;3 Proof of Theorem 2.1;169
8.4;4 Proof of Theorem 2.2;174
8.5;5 Proof of Theorem 2.3;177
8.6;References;178
9;Pythagorean mathematical idealism and the framing of economic and political theory;179
9.1;1 Introduction;179
9.2;2 Pythagoras and his secret societies;180
9.3;3 Early use of mathematics for rational administration;181
9.4;4 Plato's dedication to rational ideal forms;183
9.5;5 The Chaldean tradition of efficient administration;184
9.6;6 Bureaucratic individualism and dispute resolution;186
9.7;7 Plato's assimilation of Pythagorean thought;187
9.8;8 Solving the problem of irrational numbers: the dyad of the greater and the smaller;188
9.9;9 Prometheus and fair division;192
9.10;10 The process of arriving at settlements: the dyad;194
9.11;11 Aristotle's analysis of exchange and the harmonic proportion;195
9.12;12 In summary;199
9.13;References;200
10;Subject Index
;202
11;Instructions for Authors
;207