Advances in mathematical economics

Shigeo Kusuoka, Akira Yamazaki4431777830, 9784431777830, 9784431777847

A lot of economic problems can 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 were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers. Members of the editorial board of this series consists of following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), A. Yamazaki (Hitotsubashi Univ.) – Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier II), F. H. Clarke (Univ. Lyon I), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Fukuoka Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama National Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Hitotsubashi Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), K. Kamiya (Univ. Tokyo), K. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), T. Maruyama (Keio Univ.), H. Matano (Univ. Tokyo), K. Nishimura (Kyoto Univ.), M. K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

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Table of contents :
Advances in Mathematical Economics……Page 2
Advances in Mathematical Economics Volume 11……Page 4
ISBN 978-4-431-77783-0……Page 5
Table of Contents……Page 6
Optimal hedging strategies on asymmetric functions……Page 7
Introduction……Page 8
Setup……Page 10
The unique existence of the solution……Page 12
References……Page 16
Introduction……Page 17
Notation and preliminaries……Page 19
Tightness conditions for sequences of multifunctions……Page 22
Integrability results for the sequential weak upper limit……Page 27
The case of multifunctions with values in a dual space……Page 40
References……Page 49
Introduction……Page 51
Basic definitions and results……Page 55
Common ingredients……Page 59
Example of the failure of core convergence……Page 60
Example with no Walrasian equilibrium in the limit……Page 63
Example with a Walrasian equilibrium in the limit……Page 66
Conclusion……Page 68
References……Page 81
Introduction……Page 83
Preliminaries……Page 84
General Lorenz dominance and zero-sum two-person games……Page 87
Distance and binary relation derived from values of games……Page 89
Distances between typical income distributions……Page 92
References……Page 99
Introduction……Page 100
Preliminary notions and results……Page 101
Main results……Page 103
Proofs……Page 104
References……Page 108
Introduction……Page 110
Information and knowledge……Page 112
Economy with RT-information structure……Page 113
Price system and rational expectations equilibrium……Page 114
Welfare in an economy with knowledge……Page 115
Example……Page 116
Concluding remarks……Page 118
References……Page 121
Introduction……Page 122
A dynamic model of the firm……Page 126
Model framework……Page 127
Optimality criteria……Page 128
Boundary conditions……Page 130
Optimal behavior for t[,)……Page 132
Optimal behavior for t[0,]……Page 134
The short run and the delivery period……Page 136
The delivery period and the steady state……Page 137
Variable factor inputs……Page 139
Additional fixed state variables……Page 141
Concluding remarks……Page 144
The delivery period……Page 146
The short run……Page 148
References……Page 149
Introduction……Page 151
The lattice-theoretic approach……Page 153
The contraction approach……Page 155
Linear representation problem……Page 156
Link between the contraction approach and DDB……Page 157
References……Page 159
Subject Index……Page 160