The Neyman–Pearson lemma under <i>g</i>-probability

Shaolin Ji; Xun Yu Zhou

doi:10.1016/j.crma.2007.12.007

Probability Theory

The Neyman–Pearson lemma under g-probability

Presented by: Paul Deheuvels

Shaolin Ji ¹; Xun Yu Zhou ^2,³

¹ School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
² Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
³ Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 209-212.

Abstract
Résumé

The Neyman–Pearson fundamental lemma is generalized under g-probability. With convexity assumptions, a sufficient and necessary condition which characterizes the optimal randomized tests is obtained via a maximum principle for stochastic control.

Le lemme fondamental de Neyman–Pearson est généralisé au cas de g-probabilités. Sous des hypothèses de convexité, une condition suffisante et nécessaire caractérisant le test randomisé optimal est obtenue au moyen du principe du maximum dans le cadre du contrôle stochastique.

Received: 2007-09-06
Accepted: 2007-12-11
Published online: 2008-01-10

DOI: 10.1016/j.crma.2007.12.007

Author's affiliations:

Shaolin Ji ¹; Xun Yu Zhou ^{2, 3}

¹ School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
² Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
³ Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

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Shaolin Ji; Xun Yu Zhou. The Neyman–Pearson lemma under g-probability. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 209-212. doi : 10.1016/j.crma.2007.12.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.12.007/

References
Cited by

[1] P. Boyle; W. Tian Portfolio management with constraints, Math. Finance, Volume 17 (2007), pp. 319-343

[2] Z. Chen; L. Epstein Ambiguity, risk and asset returns in continuous time, Econometrica, Volume 70 (2002), pp. 1403-1443

[3] Z. Chen; R. Kulperger Minimax pricing and Choquet pricing, Insurance: Mathematics and Economics, Volume 38 (2006), pp. 518-528

[4] J. Cvitanic; I. Karatzas Generalized Neyman–Pearson lemma via convex duality, Bernoulli, Volume 7 (2001), pp. 79-97

[5] N. El Karoui; S. Peng; M.C. Quenez Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997), pp. 1-71

[6] N. El Karoui; S. Peng; M.-C. Quenez A dynamic maximum principle for the optimization of recursive utilities under constraints, Ann. Appl. Probab., Volume 11 (2001), pp. 664-693

[7] H. Föllmer; P. Leukert Efficient hedging: cost versus shortfall risk, Finance Stochast., Volume 4 (2000), pp. 117-146

[8] E. Gianin Risk measures via g-expectations, Insurance: Mathematics and Economics (2006), pp. 19-34

[9] S. Helmut Mathematical Theory of Statistics, Walter de Gruyter & Co., Berlin, 1985

[10] P. Huber; V. Strassen Minimax tests and the Neyman–Pearson lemma for capacities, Ann. Statist., Volume 1 (1973), pp. 251-263

[11] S. Ji, S. Peng, Terminal perturbation method for the backward approach to continuous-time mean-variance portfolio selection, Stochastic Process. Appl. (2008), , in press | DOI

[12] S. Ji; X. Zhou A maximum principle for stochastic optimal control with terminal state constraints, and its applications, Commun. Inf. Systems, Volume 6 (2006), pp. 321-337 (a special issue dedicated to Tyrone Duncan on the occasion of his 65th birthday)

[13] S. Peng Backward stochastic differential equations and related g-expectation (N. El Karoui; L. Mazliak, eds.), Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 141-159

Cited by Sources:

^⁎ The authors thank the partial support from the National Basic Research Program of China (973 Program, No. 2007CB814900), the RGC Earmark Grant No. 418606, and a start-up fund at Oxford.

^⁎⁎ This Note is the succinct version of a text on file for five years in the Academy Archives.

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