Advances in Mathematical Economics Volume 14 (eBook)

The Workshop on Mathematical Economics 2009 Tokyo, Japan, November 2009 Revised Selected Papers

Shigeo Kusuoka, Toru Maruyama (Herausgeber)

eBook Download: PDF

2010 | 2011
VIII, 232 Seiten
Springer Tokyo (Verlag)
978-4-431-53883-7 (ISBN)

Infos

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.

Inhalt

Preface 
6 
Table of Contents 
7 
How much can investors discount? 9
1 Introduction 9
2 Shortfall risk measures 11
3 Complete market case 14
4 Diffusion type models 19
4.1 Black–Scholes model 21
4.2 American type claims 22
References 24
Variational analysis and mathematical economics 2: Nonsmooth regular economies 25
1 Introduction 25
2 The model 28
3 Classical regularity concept and Debreu's theorem 30
4 Regularity in variational analysis 32
5 Semi-algebraic and definable functions and mappings 36
6 Semi-algebraic model of an exchange economy 41
References 45
An overview of turnpike theory: towards the discounted deterministic case 47
1 Introduction 48
2 Relevant results in continuous time 55
3 The basic model in discrete time 58
4 Smooth felicities and asymptotic stability 60
4.1 Scheinkman's ``neighborhood" stability theorem 60
4.2 Refinements of the ``neighborhood" theorem 62
5 The theory in non-smooth environments 64
5.1 Theorems under refined interiority assumptions 64
5.2 McKenzie's ``neighborhood turnpike" theorem 65
6 Particular undiscounted cases: the RSS model 66
6.1 A theorem on asymptotic stability 67
6.2 Classical turnpike theorems 68
7 Particular undiscounted cases: the MW model 68
7.1 A theorem on asymptotic stability 70
7.2 Classical turnpike results 70
8 Conclusion 70
References 72
Stock price process and long memory in trade signs 76
1 Introduction 76
2 Description of the model and statement of result 79
3 Abstract polymer expansion 82
4 Proof of result 89
References 98
Extended second welfare theorem for nonconvex economies with infinite commodities and public goods 100
1 Introduction 101
2 Nonconvex economies with private and public goods 105
2.1 The model 105
2.2 Qualification conditions 107
3 Tools of variational analysis 110
3.1 Generalized normals 110
3.2 Extremal principle 113
4 Approximate versions of the extended second welfaretheorem for economies with public goods 116
5 Exact versions of the extended second welfare theorem for economies with public goods 122
6 Nonconvex economies with ordered commodity space 127
References 131
Partial hedging for defaultable claims 134
1 Introduction 134
2 Model 136
3 Maximizing the probability of the super-hedge 139
4 Minimizing the expected loss of hedging 144
5 Case of non-zero recovery rate 149
6 Conclusion 150
References 151
Robust utility maximization with unbounded random endowment 153
1 Introduction 153
2 Main results 155
2.1 Setup 155
Utility functions and conjugate 155
Measures and V-divergences 156
Random endowment 158
2.2 Main theorems 159
2.3 Indifference valuation 162
3 Duality 166
4 Solution to the dual problem 169
4.1 Preliminary estimates 170
4.2 Existence of a solution 173
4.3 Variational characterizations 175
5 Optimal strategy 180
5.1 Proof of Theorem 2.8 (a) 180
5.2 Proof of Theorem 2.8 (b), (c) 181
References 184
A time-embedded approach to economic equilibrium with incomplete financial markets 188
1 Introduction 189
2 Background 190
3 Incorporating an uncertain future 192
4 Existence of equilibrium 196
5 Pattern of development 199
References 200
Strong convergence theorems by hybrid methods for nonexpansive mappings with equilibrium problems in Banach spaces 202
1 Introduction 203
2 Preliminaries 204
3 Semi-positively homogeneous nonexpansive mappings 208
4 Strong convergence theorems 210
References 220
Appendixes 
224 
Programme 224
Photographs 227
Subject Index 229
Instructions for Authors 233

Produkt-Details

• Erscheint lt. Verlag: 29.11.2010
• Reihe/Serie: Advances in Mathematical Economics
• Reihe/Serie: Advances in Mathematical Economics
• Zusatzinfo: VIII, 232 p.
• Verlagsort: Tokyo
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Studium ► 1. Studienabschnitt (Vorklinik) ► Biochemie / Molekularbiologie
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie
• Schlagworte: Economic Theory • Finance • Probability • Static Economics • stochastic analysis
• ISBN-10: 4-431-53883-6 / 4431538836
• ISBN-13: 978-4-431-53883-7 / 9784431538837