Locally Coherent Rates of Exchange
A theory of coherence is formulated for rates of exchange between events. The theory can be viewed as a generalization of de Finetti's theory of coherence as well as the theory of conditional coherence. Coherent rates of exchange on a fixed Boolean algebra are in one-to-one correspondence with...
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| Veröffentlicht in: | The Annals of statistics 1989-09, Vol.17 (3), p.1394-1408 |
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| container_title | The Annals of statistics |
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| creator | Armstrong, Thomas E. Sudderth, William D. |
| description | A theory of coherence is formulated for rates of exchange between events. The theory can be viewed as a generalization of de Finetti's theory of coherence as well as the theory of conditional coherence. Coherent rates of exchange on a fixed Boolean algebra are in one-to-one correspondence with finitely additive conditional probability measures on the algebra. Results of Renyi and Krauss on conditional probability spaces are used to show that coherent rates of exchange are generated by ordered families of finitely additive measures, possibly infinite measures. This provides an interpretation of improper prior distributions in terms of coherence. An extension theorem is proved and gives a generalization of extension theorems for finitely additive probability measures. |
| doi_str_mv | 10.1214/aos/1176347278 |
| format | Article |
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An extension theorem is proved and gives a generalization of extension theorems for finitely additive probability measures.</description><subject>60A05</subject><subject>62A15</subject><subject>Algebra</subject><subject>Bookmaking</subject><subject>Coherence</subject><subject>Coherence theory</subject><subject>Conditional probabilities</subject><subject>conditional probability</subject><subject>Exact sciences and technology</subject><subject>Exchange rates</subject><subject>finite additivity</subject><subject>Foreign exchange rates</subject><subject>General topics</subject><subject>improper priors</subject><subject>Lebesgue measures</subject><subject>Mathematical induction</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNplUM9LwzAUDqLgnF49eSiCx255SZo0N6XMH1AQxJ1Lmry6jrqMpIL771dZ2Q6ePnjfL75HyC3QGTAQc-PjHEBJLhRT-RmZMJB5mmspz8mEUk3TjEtxSa5iXFNKMy34hNyX3pqu2yWFX2HATZ98mB5j4ptk8WtXZvOF1-SiMV3EmxGnZPm8-Cxe0_L95a14KlPLQfWpQO60HpqR2ZqhcdLVos6QI4q6diprMqcZKqosOCtFwzlYXVNHYaBywafk8ZC7DX6Ntscf27Wu2ob224Rd5U1bFctyvI4wbK5Om4eI2SHCBh9jwOboBlr9Pem_4WHsNHH4QxPMxrbx5NJK5RT4oLs76Nax9-HIMyZAccb3vzNwng</recordid><startdate>19890901</startdate><enddate>19890901</enddate><creator>Armstrong, Thomas E.</creator><creator>Sudderth, William D.</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19890901</creationdate><title>Locally Coherent Rates of Exchange</title><author>Armstrong, Thomas E. ; Sudderth, William D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c317t-4e3d99278e2cb2ead6db4b5e3ee4bbd75f5d92e707c1dc64f331c9b0d015f5843</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>60A05</topic><topic>62A15</topic><topic>Algebra</topic><topic>Bookmaking</topic><topic>Coherence</topic><topic>Coherence theory</topic><topic>Conditional probabilities</topic><topic>conditional probability</topic><topic>Exact sciences and technology</topic><topic>Exchange rates</topic><topic>finite additivity</topic><topic>Foreign exchange rates</topic><topic>General topics</topic><topic>improper priors</topic><topic>Lebesgue measures</topic><topic>Mathematical induction</topic><topic>Mathematical theorems</topic><topic>Mathematics</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Armstrong, Thomas E.</creatorcontrib><creatorcontrib>Sudderth, William D.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Armstrong, Thomas E.</au><au>Sudderth, William D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Locally Coherent Rates of Exchange</atitle><jtitle>The Annals of statistics</jtitle><date>1989-09-01</date><risdate>1989</risdate><volume>17</volume><issue>3</issue><spage>1394</spage><epage>1408</epage><pages>1394-1408</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>A theory of coherence is formulated for rates of exchange between events. 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| source | JSTOR Mathematics & Statistics; Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 60A05 62A15 Algebra Bookmaking Coherence Coherence theory Conditional probabilities conditional probability Exact sciences and technology Exchange rates finite additivity Foreign exchange rates General topics improper priors Lebesgue measures Mathematical induction Mathematical theorems Mathematics Probability and statistics Sciences and techniques of general use Statistics |
| title | Locally Coherent Rates of Exchange |
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