The maximum maximum of a martingale

David G. Hobson

Séminaire de probabilités de Strasbourg (1998)

  • Volume: 32, page 250-263

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Hobson, David G.. "The maximum maximum of a martingale." Séminaire de probabilités de Strasbourg 32 (1998): 250-263. <http://eudml.org/doc/113988>.

@article{Hobson1998,
author = {Hobson, David G.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {martingale; maximum of a martingale; Hardy-Littlewood maximal measure; stochastic order},
language = {eng},
pages = {250-263},
publisher = {Springer - Lecture Notes in Mathematics},
title = {The maximum maximum of a martingale},
url = {http://eudml.org/doc/113988},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Hobson, David G.
TI - The maximum maximum of a martingale
JO - Séminaire de probabilités de Strasbourg
PY - 1998
PB - Springer - Lecture Notes in Mathematics
VL - 32
SP - 250
EP - 263
LA - eng
KW - martingale; maximum of a martingale; Hardy-Littlewood maximal measure; stochastic order
UR - http://eudml.org/doc/113988
ER -

References

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  2. [2] Azéma, J. AND Yor, M.; Une solution simple au problème de Skorokhod, Séminaire de Probabilités, XIII, 90-115, 1979. Zbl0414.60055MR544782
  3. [3] Bertoin, J. AND Le Jan, Y.; Representation of measures by balayage from a regular recurrent point, Annals of Probability, 20, 538-548, 1992. Zbl0749.60038MR1143434
  4. [4] Blackwell, D. AND Dubins, L.D.; A Converse to the Dominated Convergence Theorem, Illinois Journal of Mathematics, 7, 508-514, 1963. Zbl0146.37503MR151572
  5. [5] Chacon, R. AND Walsh, J.B.; One-dimensional potential embedding, Séminaire de Probabilités, X, 19-23, 1976. Zbl0329.60041MR445598
  6. [6] Dubins, L.D.; On a theorem of Skorokhod, Annals of Mathematical Statistics, 39, 2094-2097, 1968. Zbl0185.45103MR234520
  7. [7] Dubins, L.D.AND Gilat, D.; On the distribution of maxima of martingales, Proceedings of the American Mathematical Society, 68, 337-338, 1978. Zbl0351.60049MR494473
  8. [8] Hobson, D.G.; Robust hedging of the lookback option, To appear in Finance and Stochastics, 1998. Zbl0907.90023
  9. [9] Kertz, R.P.AND Rösler, U.; Martingales with given maxima and terminal distributions, Israel J. Math., 69, 173-192, 1990. Zbl0743.60046MR1045372
  10. [10] Meyer, P.A.; Probability and Potentials, Blaidsell, Waltham, Mass., 1966. Zbl0138.10401MR205288
  11. [11] Perkins, E.; The Cereteli-Davis solution to the H1-embedding problem and an optimal embedding in Brownian motion, Seminar on Stochastic Processes, 1985, Birkhauser, Boston, 173-223, 1986. Zbl0607.60071MR896743
  12. [12] Rogers, L.C.G.; Williams' characterisation of the Brownian excursion law: proof and applications, Séminaire de Probabilités, XV, 227-250, 1981. Zbl0462.60078MR622566
  13. [13] Rogers, L.C.G.; A guided tour through excursions, Bull. London Math. Soc., 21, 305-341, 1989. Zbl0689.60075MR998631
  14. [14] Rogers, L.C.G.; The joint law of the maximum and the terminal value of a martingale, Prob. Th. Rel. Fields, 95, 451-466, 1993. Zbl0794.60042MR1217446
  15. [15] Rösler, U.; Personal communication. 
  16. [16] Strassen, V.; The existence of probability measures with given marginals, Ann. Math. Statist., 36, 423-439, 1965. Zbl0135.18701MR177430
  17. [17] Vallois, P.; Sur la loi du maximum et du temps local d'une martingale continue uniformément intégrable, Proc. London Math. Soc., 3, 399-427, 1994. Zbl0807.60041MR1281971

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