NDLI: A generalized Neyman–Pearson lemma for g-probabilities

Content Provider	Springer Nature Link
Author	Ji, Shaolin Zhou, Xun Yu
Copyright Year	2009
Abstract	This paper is concerned with hypothesis tests for g-probabilities, a class of nonlinear probability measures. The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. The latter is solved with a stochastic maximum principle approach. Neyman–Pearson type results are thereby derived for the original problem with both simple and randomized tests. It turns out that the likelihood ratio in the optimal tests is nothing else than the ratio of the adjoint processes associated with the maximum principle. Concrete examples, ranging from the classical simple tests, financial market modelling with ambiguity, to super- and sub-pricing of contingent claims and to risk measures, are presented to illustrate the applications of the results obtained.
Ending Page	669
Page Count	25
Starting Page	645
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	148
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-09-16
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Backward stochastic differential equation Applications of stochastic analysis (to PDE, etc.) g-probability/expectation Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Neyman–Pearson lemma Quantitative Finance Stochastic maximum principle Hypothesis test Statistics for Business/Economics/Mathematical Finance/Insurance Optimal stochastic control Operations Research/Decision Theory Stochastic ordinary differential equations Mathematical Biology in General
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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