Nonlinear and Convex Analysis in Economic Theory

ISBN-13: 9783540587675 / Angielski / Miękka / 1995 / 306 str.

Toru Maruyama;Wataru Takahashi

Opis

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.), and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza- tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the- ories. Although our special emphasis was laid upon "nonlinearity" and "con- vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark- able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings: 1) Nonlinear Dynamical Systems and Business Fluctuations, . 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.

Spis treści

The Bargaining Set in Large Finite NTU Exchange Economies.- Epi-convergence of Integral Functionals Defined on the Space of Measures.- Multiple—Phase Economic Dynamics.- Stabilizing Unstable Systems.- On First Order Sufficient Conditions for Constrained Optima.- Expectations Driven Nonlinear Business Cycles.- Cores, Almost Competitive Prices, and the Approximate Optimality of Walrasian Allocations in Discrete Spaces.- Cooperative Processing of Information.- A Survey of Stochastic Differential Equations.- Stability and Oscillations in a Dynamical Kaldorian Model.- On Large Games with Finite Actions: A Synthetic Treatment.- On a Method Constructing Morse Flows.- On Covering Theorems of a Simplex and Their Generalizations.- Positive Nonlinear Systems in Economics.- Option Replication Cost with Transaction Costs.- Fixed Paint and Finite Dimensional Invariant Subspace Properties for Semigroups and Amenability.- Pricing of Bonds and their Derivatives with Multi-factor Stochastic Interest Rates: A Note.- Non-Linearity and Business Cycles in a Two-Sector Equilibrium Model: An Example with Cobb-Douglas Production Functions.- Methods of Duals in Nonlinear Analysis — Lipschitz Duals of Banach Spaces and Some Applications —.- Swimming below Icebergs.- Comparative Statics and Algorithms for Finding Economic Equilibria.- Classification of chaos and a large deviation theory for compact dynamical systems.- On a Perturbation of Dynamic Programming.- Bargaining Sets in Continuum Economies.- Conference Information.