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
[Lemme de Neyman–Pearson généralisé pour les g-espérances]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2007-09-06
Accepté le : 2007-12-11
Publié le : 2008-01-10

DOI : 10.1016/j.crma.2007.12.007

Affiliations des auteurs :

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

@article{CRMATH_2008__346_3-4_209_0,
     author = {Shaolin Ji and Xun Yu Zhou},
     title = {The {Neyman{\textendash}Pearson} lemma under \protect\emph{g}-probability},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {209--212},
     publisher = {Elsevier},
     volume = {346},
     number = {3-4},
     year = {2008},
     doi = {10.1016/j.crma.2007.12.007},
     language = {en},
}

TY  - JOUR
AU  - Shaolin Ji
AU  - Xun Yu Zhou
TI  - The Neyman–Pearson lemma under g-probability
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 209
EP  - 212
VL  - 346
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2007.12.007
LA  - en
ID  - CRMATH_2008__346_3-4_209_0
ER  -

%0 Journal Article
%A Shaolin Ji
%A Xun Yu Zhou
%T The Neyman–Pearson lemma under g-probability
%J Comptes Rendus. Mathématique
%D 2008
%P 209-212
%V 346
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2007.12.007
%G en
%F CRMATH_2008__346_3-4_209_0

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/

Bibliographie
Cité par

[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

Chuanfeng Sun; Shaolin Ji The Neyman–Pearson lemma for convex expectations, Mathematical Control and Related Fields, Volume 15 (2025) no. 1, p. 143 | DOI:10.3934/mcrf.2024004
Qingmeng Wei The optimal control problem with state constraints for forward–backward stochastic systems with jumps, IMA Journal of Mathematical Control and Information (2015), p. dnv053 | DOI:10.1093/imamci/dnv053
Li Li The Optimal Portfolio Selection Model underg-Expectation, Abstract and Applied Analysis, Volume 2014 (2014), p. 1 | DOI:10.1155/2014/426036
Qingmeng Wei; Xinling Xiao An Optimal Control Problem of Forward-Backward Stochastic Volterra Integral Equations with State Constraints, Abstract and Applied Analysis, Volume 2014 (2014), p. 1 | DOI:10.1155/2014/432718
Qingmeng Wei The Optimal Control Problem with State Constraints for Fully Coupled Forward-Backward Stochastic Systems with Jumps, Abstract and Applied Analysis, Volume 2014 (2014), p. 1 | DOI:10.1155/2014/216053
Libo Ding; Bangyi Li; Suling Feng; Ming Gao Research on Multiprincipals Selecting Effective Agency Mode in the Student Loan System, Mathematical Problems in Engineering, Volume 2014 (2014) no. 1 | DOI:10.1155/2014/835254
Shaolin Ji; Xun Yu Zhou A generalized Neyman–Pearson lemma for g-probabilities, Probability Theory and Related Fields, Volume 148 (2010) no. 3-4, p. 645 | DOI:10.1007/s00440-009-0244-4

Cité par 7 documents. Sources : Crossref

^⁎ 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.

Commentaires - Politique