Probability Theory
The Neyman–Pearson lemma under g-probability
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 209-212.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.12.007
Ji, Shaolin 1; Zhou, Xun Yu 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 = {Ji, Shaolin and Zhou, Xun Yu},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.12.007/}
}
TY  - JOUR
AU  - Ji, Shaolin
AU  - Zhou, Xun Yu
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
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.12.007/
DO  - 10.1016/j.crma.2007.12.007
LA  - en
ID  - CRMATH_2008__346_3-4_209_0
ER  - 
%0 Journal Article
%A Ji, Shaolin
%A Zhou, Xun Yu
%T The Neyman–Pearson lemma under g-probability
%J Comptes Rendus. Mathématique
%D 2008
%P 209-212
%V 346
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.12.007/
%R 10.1016/j.crma.2007.12.007
%G en
%F CRMATH_2008__346_3-4_209_0
Ji, Shaolin; Zhou, Xun Yu. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.12.007/

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

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

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

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

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

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

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

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

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

[10] Huber, P.; Strassen, V. 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] Ji, S.; Zhou, X. 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] Peng, S. Backward stochastic differential equations and related g-expectation (El Karoui, N.; Mazliak, L., 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.