Far East Journal of Theoretical Statistics
Volume 20, Issue 2, Pages 241 - 256
(November 2006)
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JENSEN’S INEQUALITY FOR g-EXPECTATION
Fan Sheng-Jun (P. R. China)
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Abstract: In 2003, Jiang gave a sufficient condition under which Jensen’s
inequality of bivariate function for g-expectation holds under the
situation that g does not depend on y, and in 2004, he gave a
sufficient and necessary condition under which Jensen’s inequality for g-expectation
holds in general under the situation that g does not depend on y
and is continuous in t. In this paper, after investigating some
relationship between the generator g and the conditional g-expectation
system, under the most elementary conditions with respect to g-expectation,
a sufficient and necessary condition under which Jensen’s inequality of
bivariate function for g-expectation holds is obtained. At the same time,
it is proved that under the condition g is continuous in t, if
Jensen’s inequality for g-expectation holds in general, then g
must not depend on y. |
Keywords and phrases: backward stochastic differential equation, g-expectation,
Jensen’s inequality, comparison theorem, generator. |
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