A non-linear Riesz respresentation in probabilistic potential theory

Nicole El Karoui; Hans Föllmer

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 3, page 269-283
  • ISSN: 0246-0203

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El Karoui, Nicole, and Föllmer, Hans. "A non-linear Riesz respresentation in probabilistic potential theory." Annales de l'I.H.P. Probabilités et statistiques 41.3 (2005): 269-283. <http://eudml.org/doc/77845>.

@article{ElKaroui2005,
author = {El Karoui, Nicole, Föllmer, Hans},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Potential operator; Harmonic function; Optimal stopping},
language = {eng},
number = {3},
pages = {269-283},
publisher = {Elsevier},
title = {A non-linear Riesz respresentation in probabilistic potential theory},
url = {http://eudml.org/doc/77845},
volume = {41},
year = {2005},
}

TY - JOUR
AU - El Karoui, Nicole
AU - Föllmer, Hans
TI - A non-linear Riesz respresentation in probabilistic potential theory
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 3
SP - 269
EP - 283
LA - eng
KW - Potential operator; Harmonic function; Optimal stopping
UR - http://eudml.org/doc/77845
ER -

References

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  1. [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. Zbl1190.93001
  2. [2] P. Bank, Gittins indices for American options, Humboldt University of Berlin, 2004, in preparation. 
  3. [3] P. Bank, N. El Karoui, A stochastic representation theorem with applications to optimization and obstacle problems, Ann. Probab.32 (1B) (2004) 1030-1067. Zbl1058.60022MR2044673
  4. [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. Zbl1065.91022MR2021789
  5. [5] P. Bank, F. Riedel, Optimal consumption choice with intertemporal substitution, Ann. Appl. Probab.3 (2001) 755-788. Zbl1022.90045MR1865023
  6. [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. Zbl0624.60084MR898005
  7. [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. Zbl0724.31007MR1071532
  8. [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. Zbl0472.60002MR637471
  9. [9] N. El Karoui, I. Karatzas, Dynamic allocation problems in continuous time, Ann. Appl. Probab.4 (1994) 255-286. Zbl0831.93069MR1272729
  10. [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. Zbl0841.90051
  11. [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. Zbl0893.90171MR1674292
  12. [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. Zbl0302.60050MR368185
  13. [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. Zbl0218.31015MR294680
  14. [14] A.N. Shiryaev, Statistical Sequential Analysis, Amer. Math. Soc., Providence, RI, 1973. 
  15. [15] P. Whittle, Multi-armed bandits and the Gittins index, J. Roy. Statist. Soc. Ser. B42 (2) (1980) 143-149. Zbl0439.90096MR583348

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