This article introduces a new way of understanding subjective probability and its generalization to lower and upper prevision. Instead of asking whether a person is willing to pay given prices for given risky payoffs, we ask whether the person believes he can make a lot of money at those prices. If not---if the person is convinced that no strategy for exploiting the prices can make him very rich in the long run---then the prices measure his subjective uncertainty about the events involved. This new understanding justifies Peter Walley's updating principle, which applies when new information is anticipated exactly. It also justifies a weaker principle that is more useful for planning because it applies even when new information is not anticipated exactly. This weaker principle can serve as a basis for flexible probabilistic planning in event trees.
Keywords. Subjective probability, upper and lower prevision, updating, event trees
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Authors addresses:
Peter Gillett
Department of Accounting & Information Systems
School of Business - New Brunswick
RUTGERS: The State University of New Jersey
Jancie H. Levin Building
94 Rockafeller Road
Piscataway
NJ 08854-8054
USA
Glenn Shafer
Rutgers School of Business - Newark and New Brunswick
Rutgers University
180 University Avenue,
07102, Newark,New Jersey
USA
Richard Scherl
...
E-mail addresses:
| Peter Gillett | gillett@business.rutgers.edu |
| Glenn Shafer | gshafer@andromeda.rutgers.edu |
| Richard Scherl | rscherl@monmouth.edu |