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A counterexample on the continuity of conditional expectations

โœ Scribed by Alberto Alonso


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
218 KB
Volume
129
Category
Article
ISSN
0022-247X

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A necessary and sufficient condition on a sequence n nโˆˆN of ฯƒ-subalgebras that assures L p -convergence of the conditional expectations is given. This result generalizes the L p -martingales, the Fetter and the Boylan (equiconvergence) theorems.

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## Abstract Unlike the value at risk, the expected shortfall is a coherent measure of risk. In this paper, we discuss estimation of the expected shortfall of a random variable __Y__~__t__~ with special reference to the case when auxiliary information is available in the form of a set of predictors