Nonlinear and convex analysis in economic theory : [contributions to TI Tech/KES Conference on Nonlinear and Convex Analysis in Economic Theory ... Keio University, July 2-4, 1993

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. The Bargaining Set In Large Finite Ntu Exchange Economies / Robert M. Anderson -- Epi-convergence Of Integral Functionals Defined On The Space Of Measures / Charles Castaing And Vincent Jalby -- Multiple-phase Economic Dynamics / Richard H. Day -- Stabilizing Unstable Systems / Takao Fujimoto -- On First Order Sufficient Conditions For Constrained Optima / Giorgio Giorgi -- Expectations Driven Nonlinear Business Cycles / Jean-michel Grandmont -- Cores, Almost Competitive Prices, And The Approximate Optimality Of Walrasian Allocations In Discrete Spaces / Leonid Hurwicz -- Cooperative Processing Of Information / Tatsuro Ichiishi -- A Survey Of Stochastic Differential Equations / Kiyosi Itō -- Stability And Oscillations In A Dynamical Kaldorian Model / Kunio Kawamata -- On Large Games With Finite Actions : A Synthetic Treatment / M. Ali Khan And Yeneng Sun -- On A Method Constructing Morse Flows / Norio Kikuchi --^ On Covering Theorems Of A Simplex And Their Generalizations / Hidetoshi Komiya -- Positive Nonlinear Systems In Economics / Ulrich Krause -- Option Replication Cost With Transaction Costs / Shigeo Kusuoka -- Fixed Point And Finite Dimensional Invariant Subspace Properties For Semigroups And Amenability / Anthony To-ming Lau -- Pricing Of Bonds And Their Derivatives With Multi-factor Stochastic Interest Rates : A Note / Miura Ryozo And Kishino Hirohisa -- Non-linearity And Business Cycles In A Two-sector Equilibrium Model : An Example With Cobb-douglas Production Functions / Kazuo Nishimura And Makoto Yano -- Methods Of Duals In Nonlinear Analysis : Lipschitz Duals Of Banach Spaces And Some Applications / Ikuko Sawashima -- Swimming Below Icebergs / S. Simons -- Comparative Statics And Algorithms For Finding Economic Equlibria / Steve Smale -- Classification Of Chaos And A Large Deviation Theory For Compact Dynamical Systems / Yoichiro Takahashi --^ On A Perturbation Of Dynamic Programming / Kensuke Tanaka -- Bargaining Sets In Continuum Economics / Akira Yamazaki. Toru Maruyama, Wataru Takahashi, Eds. Contributions To T.i. Tech/k.e.s. Conference On Nonlinear And Convex Analysis In Economic Theory ... Keio University, July 2-4, 1993--preface. Includes Bibliographical References. Front Matter....Pages I-VIII The Bargaining Set in Large Finite NTU Exchange Economies....Pages 1-7 Epi-convergence of Integral Functionals Defined on the Space of Measures....Pages 9-23 Multiple—Phase Economic Dynamics....Pages 25-45 Stabilizing Unstable Systems....Pages 47-52 On First Order Sufficient Conditions for Constrained Optima....Pages 53-66 Expectations Driven Nonlinear Business Cycles....Pages 67-78 Cores, Almost Competitive Prices, and the Approximate Optimality of Walrasian Allocations in Discrete Spaces....Pages 79-99 Cooperative Processing of Information....Pages 101-117 A Survey of Stochastic Differential Equations....Pages 119-129 Stability and Oscillations in a Dynamical Kaldorian Model....Pages 131-148 On Large Games with Finite Actions: A Synthetic Treatment....Pages 149-161 On a Method Constructing Morse Flows....Pages 163-173 On Covering Theorems of a Simplex and Their Generalizations....Pages 175-180 Positive Nonlinear Systems in Economics....Pages 181-195 Option Replication Cost with Transaction Costs....Pages 197-202 Fixed Point and Finite Dimensional Invariant Subspace Properties for Semigroups and Amenability....Pages 203-213 Pricing of Bonds and their Derivatives with Multi-factor Stochastic Interest Rates: A Note....Pages 215-229 Non-Linearity and Business Cycles in a Two-Sector Equilibrium Model: An Example with Cobb-Douglas Production Functions....Pages 231-245 Methods of Duals in Nonlinear Analysis....Pages 247-259 Swimming below Icebergs....Pages 261-265 Comparative Statics and Algorithms for Finding Economic Equilibria....Pages 267-270 Classification of chaos and a large deviation theory for compact dynamical systems....Pages 271-273 On a Perturbation of Dynamic Programming....Pages 275-287 Bargaining Sets in Continuum Economies....Pages 289-299 Back Matter....Pages 300-312 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 optimizaƯ 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 theƯ ories. Although our special emphasis was laid upon "nonlinearity" and "conƯ vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remarkƯ 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 This volume is a collection of articles which illuminate the attractive interactions between economic theory and several disciplines of mathematical analysis. The topics to be discussed here may be classified under the following six headings: - Nonlinear Dynamical Systems and Business Fluctuations; - Fixed Point Theory; - Convex Analysis and Optimization; - Eigenvalue of Positive Operators; - Stochastic Analysis and Financial Market; - General Equilibrium Analysis