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A generalized Neyman–Pearson lemma for g-probabilities
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  • Published: 16 September 2009

A generalized Neyman–Pearson lemma for g-probabilities

  • Shaolin Ji1 &
  • Xun Yu Zhou2,3 

Probability Theory and Related Fields volume 148, pages 645–669 (2010)Cite this article

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  • 16 Citations

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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.

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Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, 250100, Jinan, China

    Shaolin Ji

  2. Mathematical Institute, The University of Oxford, 24–29 St Giles, Oxford, OX1 3LB, UK

    Xun Yu Zhou

  3. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

    Xun Yu Zhou

Authors
  1. Shaolin Ji
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  2. Xun Yu Zhou
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Correspondence to Shaolin Ji.

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Ji, S., Zhou, X.Y. A generalized Neyman–Pearson lemma for g-probabilities. Probab. Theory Relat. Fields 148, 645–669 (2010). https://doi.org/10.1007/s00440-009-0244-4

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  • Received: 03 October 2008

  • Revised: 05 August 2009

  • Published: 16 September 2009

  • Issue Date: November 2010

  • DOI: https://doi.org/10.1007/s00440-009-0244-4

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Keywords

  • Backward stochastic differential equation
  • g-probability/expectation
  • Hypothesis test
  • Neyman–Pearson lemma
  • Stochastic maximum principle

Mathematics Subject Classification (2000)

  • 60H10
  • 60H30
  • 93E20
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