Advances in Mathematical Economics Volume 14 (eBook)

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