数理解析研究所講究録 1215

経済の数理解析

京都大学数理解析研究所

2 0 0 1年 6月

Preface

This volume is acollection of papers presented at the symposium on mathematical
economics sponsored by the Roeearch Institute for Mathematical Sciences, Kyoto
University, which was held during December $8\sim 10,$ 2000.
On behalf of the programme committee, I would like to extend my cordial thanks toto
all ffie participants of the symposium for their sincere and constructive$\infty \mathrm{n}\mathrm{t}\mathrm{r}\mathrm{l}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$our project.
We can safely say that maffiemafical reasonings have been playing amuch moreindispensable roles in economic theory than in any other discipline of social sciences.
theory wiffi peculiar
There seems to be several reasons which have endowed$\mathrm{e}\infty \mathrm{n}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}$mathematical characters.
First of all, many economic phenomena pemit expressions in terms of quantitative
languages.
We have also to take account of the fact that an economy consists of ahuge numberof sectors which are entangled in a complex mamer. Economic phenomena result fromthe interactions of these interdependent component sectors. Keir mutual relation is socomplicated that an ordinary language and acasual way of thinking have only very limited
abilities to describe and analyze economic phenomena. It is quite easy for anyone toimagine serious confusions which would result if we had recourse exclusively to ordinary
languages and casual reasonings. Although mathematical reasonings may somtimes seemtoo round-about for our purposes, it oertainly provides economists with simple andefficient analytical weapons.
Furthermore economists have been suffering from ffie diffIculty of controlled
experiments in their researches. That is exactly why much importance has been attached torigorous speculative experiments in economic ffieory. So called “axiomatic method”
developed in Vienna during ffie inter-war period should be regarded as being promoted by
the same view and recognition under ffie influence of D.Hilbert.
Iwould be pleased very much if our symposium could contribute to widening anddeepening of ffie mathematical foundations in economic theory.
ToruMaruyama

経済の数理解析

Maffiematical Economics
研究集会報告集2000 年 12 月 8 日 \sim 1 2 月 10 日
研究代表者

丸山

徹 (Toru Mamyma)

目次

I. Presidential Address
1. On aProblem of Proving ffie Existence of an Equilibrium in aLarge Economy
朝 ffiout Free Disposal: Aproblem of apurely fmitely additive measure arisingfiom ffie Fatou’s lemma in several dimensions——————————————————l山崎

一橋大・経済学

昭 (Akira Ymazaki)

Analytical Foundations of Economic Theory
2. On Ergodicity of some TAR(2) PrOcesses———————————————————-14$\mathrm{n}$.

東大・経済国友直人 (Naoto Kunitomo)

3. ADeterministic Economy Generates aStochastic Process: An Extended Abstract———30
神戸大・経済経営研究所

上東貴志 (Takashi Kamihigashi)

4. WHAT DIFFERENTIATES STATIONARY STOCHASTIC PROCESSESFROM ERGODIC ONES: ASURVEY
Univ. Montpellier IMichel Valadier$\mathrm{m}$33. Aspects of Equilibrium Theory

5. Toward Sophisticated$\mathrm{L}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}------------------------------------------------------------------rightarrow---- 53$

一橋大・経済学6.

野口雄一 (Yuic 石 Noguchi)

The Competitive Equilibrium and Pareto Optimum Allocations in the Eczonomy
朝 ffi Clubs———————————————————————————————–64
一橋大・経済学

武隈

愼–(Shin-Ichi T 威 ekuma)

N. Dynamic MacrO-economic Theory
7. Intergenerational Transfers Motivated by AlMism from Children towmds Palents———78
藤生

千葉経済大・経済裕 (Hiros 石 Fujiu)

8. Short-Run Trade Surplus Creation of aDomestic Competition POlicy————————94
慶應大・経済矢野誠 (Makoto Yano)

9. AMACRODYNAMIC MODEL OF FINANCIAL INSTABILITY————————-102
神戸大・経済足立-1-英之 (Hideyuki Adachi)

10. Optimal Growth wiffi Recursive:An Existence Result wiffiout Convexity
Assumptions——————————————————————————————–l 03$\mathrm{U}\dot{\mathrm{h}}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$法政大・経済佐柄信純 (Nobusumi Sagara)

11. On the Fate of an Education Obsessed SOciety————————————————–112
阪大・経済学

二神孝一 (Koichi Futagami)

阪府大・経済北川

章臣 (Akiomi Kitagawa)V. Mathematical Finance
12. An Asymptotic Expansion Scheme for the Optimal Portfolio for Invesbnent————–127
東大・数理科学Il高橋

明彦 (Akihiko Takahashi)

吉田朋広$\sim \mathrm{a}\mathrm{k}\mathrm{a}\mathrm{h}\mathrm{i}\mathrm{r}\mathrm{o}$Yoshida)

1 3. An equilibrium model of ffie short-term stock price behavior———————————143
一橋大・商学高岡

14. On Law Invariant Coherent Risk

浩一郎 (Koichiro Takaoka)$\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s}-------------------------------------rightarrow---------------- 158$楠岡

東大・数理科学. Game Theory
15. Reasonirr about Dominant Actions

成雄 ($\mathrm{S}\mathrm{h}\mathrm{i}\mathrm{g}\infty$

Kusuoka)$\mathrm{V}\mathrm{I}$–$\downarrow\mathrm{g}$$\mathrm{g}$Logic of Decision$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\eta \mathrm{I}-$慶應大・経済学

平瀬和基 (Kazuki Hirase)

茨城高専

松久隆 (Takashi Matsuhisa)

16. Iterated Elimination and No Trade Theorem
早大・経済学

Historical Perspecfive
1 7. Karl Menger’s

169

182
田中

久稔 (Hisatoshi Tanaka).

$\mathrm{M}\mathrm{a}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{m}\mathrm{a}\dot{\mathrm{h}}\mathrm{c}\mathrm{a}\mathrm{l}$Colloquium and Abraham Wald’s Existence Proof———195
武藤防衛大学校

功 (Isao Mutoh)

Topics in Economics
18. Basic theorefical ouflook about raeapitalization of rapid growth private companies
toward autogenious order societies developing counffies.
Fundamentals about principal’s decision making models about
recapitalization studies\sim ----------------------------------------------------------------------210.

$\sim \mathrm{S}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}$(株) マーケティング総合設計研究所

-2-

逸見

彰彦 (Akihiko Hemni)