Advances in Mathematical Economics: Volume 23

Description

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. 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. Editor's Preface Contents Evolution Problems with Time-Dependent Subdifferential Operators 1 Introduction 2 Notation and Preliminaries 3 Results with Single-Valued Time-Dependent Perturbation 4 Extension to L2H([0, T]) of Subdifferential Operator ∂φ(t, ·) 5 Main Results 5.1 Existence Results for Problem (P2) 5.2 Some Variants with the Velocity in the Subdifferential 6 Applications 6.1 A Skorokhod Problem 6.2 Towards a Couple of Evolution Inclusion Involving Fractional Differential Equation 6.3 A Second Order Evolution Inclusion References Infinite Horizon Optimal Control of Non-Convex Problems Under State Constraints 1 Introduction 2 Preliminaries and Notations 3 Value Function of the Infinite Horizon Problem 4 Upper Semicontinuity of the Value Function 5 Relaxation in the Absence of State Constraints 6 Relaxation in the Presence of State Constraints 7 Relation to a Finite Horizon Bolza Problem 8 Maximum Principle and Sensitivity Relation 9 Hamilton–Jacobi Equation References The Nonemptiness of the Inner Core 1 Introduction 2 NTU Games and the Inner Core 3 Characterization of Efficient Surface with Strictly Positive Normal Vectors 4 Nonemptiness of the Inner Core 5 NTU Games Generated by Exchange Economies 6 Concluding Remarks References Complicated Dynamics and Parametric Restrictions in the Robinson-Solow-Srinivasan (RSS) Model 1 Introduction 2 The Two-Sector RSS Model 2.1 Constructs from Dynamic Programming 2.2 The Modified Golden Rule 2.3 A Failure of Strict Concavity 2.4 Basic Properties of the OPC 3 An Explicit Solution of the OPF 4 Optimal Topological Chaos 5 Technological Restrictions for Optimal Topological Chaos 5.1 Technological Restrictions for Optimal Period-Three Cycles 5.2 Technological Restrictions for Optimal Turbulence 6 Discount-Factor Restrictions for Optimal Topological Chaos 6.1 Discount-Factor Restrictions for Optimal Period-Three Cycles 6.2 Discount-Factor Restrictions for Optimal Turbulence 7 Concluding Remarks Appendix Lemmata for the Proof of Proposition 7 Lemmata for the Proof of Proposition 8(ii) A Monotone Property A Straight-Down-the-Turnpike Property An OPF for a Special Case Proof of Proposition 8(ii) References Some Regularity Estimates for Diffusion Semigroups with Dirichlet Boundary Conditions 1 Introduction 2 Part I: Horizontal Direction 2.1 Normed Spaces and Interpolation 2.2 Basic Results 2.3 Main Lemma 2.4 Proof of Theorem 3(1) 2.5 Dual Operators 3 Part II: Vertical Direction 3.1 Banach Spaces 3.2 Some Normed Spaces 3.3 Differential Operators and Basic Equality 3.4 L∞-Estimate 3.5 L1-Estimate 3.6 Proof of Theorem 2 References Disintegration of Young Measures and Nonlinear Analysis 1 Introduction 2 Disintegrations 2.1 Measurable Family of Measures 2.2 The Dual of L1(Ω, C∞(X, R)) 2.3 Disintegration Theorem (A) 2.4 Auxiliary Preparations 2.5 Disintegration Theorem (B) 2.6 Conditional Probabilities 3 Convergence 3.1 Narrow Topology 3.2 Convergence of Young Measures Associated with Measurable Functions 3.3 Tightness 3.4 Multiple Young Measures 3.5 Simple Variational Problems via Theory of Young Measures 4 Continuity of Nonlinear Integral functionals 4.1 Roles of Uniform Integrability 4.2 Castaing–Clauzure Theorem 4.3 Towards Calculus of Variations References Complete List of Works Published in Advances in Mathematical Economics Vol. 1–23 Index