A non-linear Riesz respresentation in probabilistic potential theory
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 269-283.
@article{AIHPB_2005__41_3_269_0,
     author = {El Karoui, Nicole and F\"ollmer, Hans},
     title = {A non-linear Riesz respresentation in probabilistic potential theory},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {269--283},
     publisher = {Elsevier},
     volume = {41},
     number = {3},
     year = {2005},
     doi = {10.1016/j.anihpb.2004.07.004},
     zbl = {1078.60058},
     mrnumber = {2139020},
     language = {en},
     url = {www.numdam.org/item/AIHPB_2005__41_3_269_0/}
}
El Karoui, Nicole; Föllmer, Hans. A non-linear Riesz respresentation in probabilistic potential theory. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 269-283. doi : 10.1016/j.anihpb.2004.07.004. http://www.numdam.org/item/AIHPB_2005__41_3_269_0/

[1] P. Bank, Singular control of optional random measures - stochastic optimization and representation problems arising in the microeconomic theory of intertemporal consumption choice, Ph.D. thesis, Humboldt University of Berlin, 2000. | Zbl 1190.93001

[2] P. Bank, Gittins indices for American options, Humboldt University of Berlin, 2004, in preparation.

[3] P. Bank, N. El Karoui, A stochastic representation theorem with applications to optimization and obstacle problems, Ann. Probab. 32 (1B) (2004) 1030-1067. | MR 2044673 | Zbl 1058.60022

[4] P. Bank, H. Föllmer, American options, multi-armed bandits, and optimal consumption plans: a unifying view, in: Paris-Princeton Lectures on Mathematical Finance 2002, Lecture Notes in Math., vol. 1814, Springer, Berlin, 2003, pp. 1-42. | MR 2021789 | Zbl 1065.91022

[5] P. Bank, F. Riedel, Optimal consumption choice with intertemporal substitution, Ann. Appl. Probab. 3 (2001) 755-788. | MR 1865023 | Zbl 1022.90045

[6] C. Dellacherie, P. Meyer, Probabilités et potentiel, Chapitres XII-XVI : Théorie du potentiel associée à une résolvante, Théorie des processus de Markov, Hermann, Paris, 1987. | MR 898005 | Zbl 0624.60084

[7] C. Dellacherie, Théorie des processus de production. Modèles simples de la théorie du potentiel non linéaire, in: Séminaire de Probabilités XXV, Lecture Notes in Math., vol. 1426, Springer, Berlin, 1990, pp. 52-104. | EuDML 113747 | Numdam | MR 1071532 | Zbl 0724.31007

[8] N. El Karoui, Les aspects probabilistes du contrôle stochastique, in: Ninth Saint Flour Probability Summer School - 1979 (Saint Flour, 1979), Lecture Notes in Math., vol. 876, Springer, Berlin, 1981, pp. 73-238. | MR 637471 | Zbl 0472.60002

[9] N. El Karoui, I. Karatzas, Dynamic allocation problems in continuous time, Ann. Appl. Probab. 4 (1994) 255-286. | MR 1272729 | Zbl 0831.93069

[10] N. El Karoui, I. Karatzas, The optimal stopping problem for a general American put-option, in: Davis M. (Ed.), Mathematical Finance, Springer, Berlin, 1995, pp. 63-74. | Zbl 0841.90051

[11] N. El Karoui, I. Karatzas, Synchronization and optimality for multi-armed bandit problems in continuous time, Comput. Appl. Math. 16 (2) (1997) 117-151. | MR 1674292 | Zbl 0893.90171

[12] D. Heath, Skorokhod stopping via potential theory, in: Séminaire de Probabilités VIII, Lecture Notes in Math., vol. 381, Springer, Berlin, 1974, pp. 150-154. | Numdam | MR 368185 | Zbl 0302.60050

[13] G. Mokobodzki, Quelques proprietés remarquables des opérateurs presque positifs, in: Séminaire de Probabilités IV, Lectures Notes in Math., vol. 124, Springer, Berlin, 1970, pp. 195-207. | Numdam | MR 294680 | Zbl 0218.31015

[14] A.N. Shiryaev, Statistical Sequential Analysis, Amer. Math. Soc., Providence, RI, 1973.

[15] P. Whittle, Multi-armed bandits and the Gittins index, J. Roy. Statist. Soc. Ser. B 42 (2) (1980) 143-149. | MR 583348 | Zbl 0439.90096