## Handbook of Mathematical Economics, Volume 4Kenneth Joseph Arrow, Werner Hildenbrand, Michael D. Intriligator, Hugo Sonnenschein The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. The emphasis of this fourth volume of the Handbook of Mathematical Economics is on choice under uncertainty, general equilibrium analysis under conditions of uncertainty, economies with an infinite number of consumers or commodities, and dynamical systems. The book thus reflects some of the ideas that have been most influential in mathematical economics since the appearance of the first three volumes of the Handbook.Researchers, students, economists and mathematicians will all find this Handbook to be an indispensable reference source. It surveys the entire field of mathematical economics, critically reviewing recent developments. The chapters (which can be read independently) are written at an advanced level suitable for professional, teaching and graduate-level use. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes |

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### Contents

Chapter 30 | 1523 |

Chapter 31 | 1615 |

Basic asset pricing techniques | 1625 |

Copyright | |

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agents aggregate algorithm analysis arbitrage argument asset pricing assume assumptions axiom commodity bundle commodity space compact competitive equilibrium computing cone consider constraint consumer consumption sets continuous convergence convex Debreu defined Definition denote differentiable dynamics Econometrica Economic Theory eigenvalue equations equilibrium allocations equilibrium prices equivalent example excess demand exchange economy expected utility firms fixed point GEI equilibrium given Guesnerie hence hyperfinite implies incomplete markets individual infinite dimensional initial endowment Journal of Economic Journal of Mathematical Lemma linear Mackey topology marginal cost pricing market equilibrium martingale Mas-Colell Mathematical Economics matrix maximization monopolistic competition monotonicity non-empty non-standard numeraire overlapping generations model Pareto optimal period portfolio preference relation problem production sets proof properties Proposition rational expectations result risk aversion satisfies Section sequence solution stationary stochastic subset subspace sunspot equilibria Suppose Theorem tion topology uncertainty unique University utility function utility theory vector weak topology zero