Independence, Additivity, Uncertainty

Inbunden, Engelska, 2002

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Beskrivning

This book deals with the important economic problem of uncertainty. The first attempt was to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the results was representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. The book contains all the classical results, but the main justification of the book is that the approach taken in the earlier versions was also the proper approach in generalizing from preferences, which were total preorders to preferences, which were not total or transitive. The same mathematics gives representations which are additive. It also gives decompositions where concepts of utility, probability, and uncertainty appeared. These results are new and give a solution to how uncertainty can be formalized.

Produktinformation

Utgivningsdatum:2002-11-13
Mått:155 x 235 x 22 mm
Vikt:610 g
Format:Inbunden
Språk:Engelska
Serie:Studies in Economic Theory
Antal sidor:277
Upplaga:2003
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540416838

Utforska kategorier

Nationalekonomi inom Ekonomi och Ledarskap

Recensioner i media

From the reviews of the first edition: "The most important contribution of this book is to formalize, simplify and unify concepts of uncertainity that occur in mathematical economics. ... This well-written book provides an elegant and serious introduction to the basic concepts and results of representations of preferences as sums and integrals. It discusses in detail the decomposition of preferences into utilities and probabilities. This lively presentation ... is impressive. The book will serve as an inspiration for further research and can be recommended ... ." (P.R. Parthasarathy, Zentralblatt MATH, Vol. 1080, 2006)

Innehållsförteckning

1 Introduction.- 1.1 Economics.- 1.2 Statistics.- 1.3 Mathematic.- 1.4 Summary of results.- 1.5 Applications.- I Basic Mathematics.- 2 Totally preordered sets.- 3 Preferences and preference functions.- 4 Totally preordered product sets.- 5 A subset of a product set.- 6 Mean groupoids.- 7 Products of two sets as a mean groupoid.- II Relations on Function Spaces.- 8 Totally preordered function spaces.- 9 Relations on function spaces.- III Relations on Measures.- 10 Relations on sets of probability measures.- IV Integral Representations.- 11 A general integral representation by Birgit Grodal.- 12 Special integral representations by Birgit Grodal.- V Decompositions and Uncertainty.- 13 Decompositions. Uncertainty.- 14 Uncertainty on products.- 15 Conditional uncertainty.- VI Applications.- 16 Production, utility, preference.- 17 Preferences over time.- 18 A foundation for statistics.- References.