Advances in Mathematical Economics Volume 16 [electronic resource] /
Kusuoka, Shigeo.editor.
Maruyama, Toru.editor.
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.
Description based upon print version of record.
Advances in Mathematical Economics; Table of Contents; Some applications of Birkhoff-Kingman ergodic theorem; 1 Introduction; 2 Notations and preliminaries; 3 Multivalued conditional expectation theorem; 4 Conditional expectation in a dual space; 5  An epiconvergence result; 6  Birkhoff ergodic theorem for Bochner-Gelfand-Pettis integrable multifunctions; 7 An unusual convergence for superadditive integrable process in Banach lattice; 8  Convex weakly compact valued superadditive process in L1cwk(E) (, F, P); References; Elementary form and proof of the Frobenius theorem for economists
1 Introduction2 Main Theorem; 2.1 Our Theorem; 2.2 Relationships between Our Theorem and the Usual Frobenius Theorem; 2.3 Application to the Classical Integrability Theory; 3 Proof; 3.1 Lemma; 3.2 Proof of 1); 3.3 Proof of 2); 3.4 Proof of 3); References; A remark on credit risk models and copula; 1 Introduction; 2 Preliminary results; 3 A remark on support; 4 Fundamental Relations; 5 Verification; 6 Proof of Theorem 2; 7 Remarks; 8 Proof of Proposition 16; 9 Examples of dynamical default time copula models; References; Profits and exploitation: a reappraisal; 1 Introduction
2 The Basic Model3 The classic approaches to the FMT; 3.1 Two definitions of exploitation; 3.2 Roemer's (1982) definition reconsidered; 3.3 Morishima's (1974) definition and workers' heterogeneous consumption demands; 4 A New Definition of Labour Exploitation; 5 Conclusions; References; On the equivalence between the rejective core and the dividend equilibrium: a note; 1 Introduction; 2 The model and the main theorem; 3 Proof of the main theorem; 4 Appendix; References; Discrete stochastic calculus and its applications: an expository note; 1 Introduction
2 Discrete analogue of the Itô formula3 Optimal portfolio problem; 4 Pricing of Margrabe option; 5 Discussions; References; Subject Index; Instructions for Authors
Includes bibliographical references and index.
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.
Game theory.
Game Theory, Economics, Social and Behav. Sciences.