Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Interests prices and the Barosky - Summers resolution of the Gibson paradox under the gold standard

This paper presents a structural monetary úamework featunng a demand function for non-monetary uses of gold, such as the one drawn by Barsky and Summers in their 1988 analy8ÚI of the Gibson Paradox as a natural concomitant of the gold standard period. That structural model predicts that the laws of behavior of nominal prices and interest rates are functions of the rules set by the government to command the money supply. !ta fiduciary vemon obtaina Fisherian relationships &8 particular cases. !ta gold atandard 801ution yields a modelsimilar to the Barsky and Summers model, in which interest rates are exogeneous and subject to shocb. This paper integrates governnment bonds into the analysis, treats interest rates endogenously, and ahifts the responsibility for the shocb to the government budgetary financing policies. The Gibson paradox appears as "practically" the only cl&18 of behavioral pattern open for interest rates and price movements under apure gold standard economy. Fisherian-like relationshipe are utterly ruled out.