EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 29 (2025) ESAIM: PS, 29 (2025) 357-380 References
Open Access
Issue
ESAIM: PS
Volume 29, 2025
Page(s) 357 - 380
DOI https://doi.org/10.1051/ps/2025010
Published online 05 August 2025
  1. J. Lehoczky, Formulas for stopped diffusion processes, with stopping times based on the maximum. Ann. Probab. 5 (1977) 601–608. [Google Scholar]
  2. H.M. Taylor, A stopped Brownian motion formula. Ann. Probab. 3 (1975) 234–246. [Google Scholar]
  3. P.J. Fitzsimmons, A proof of Lehoczky’s theorem on drawdowns. arXiv:2209.04695 (2022). [Google Scholar]
  4. P.J. Brockwell, Deviations from monotonicity of a Wiener process with drift. J. Appl. Prob. 11 (1974) 206–210. [Google Scholar]
  5. A.A. Malyutin, Distribution of a functional of continuous Markov processes. Cybernetics 23 (1987) 432–436. [Google Scholar]
  6. D. Williams, On a stopped Brownian motion formula of H.M. Taylor, in Séminaire de Probabilités X, Vol. 511, Springer Lecture Notes in Mathematics, edited by P. A. Meyer, Berlin, Heidelberg, New York (1976) 235–239. [Google Scholar]
  7. P. Salminen and M. Yor, On Dufresne’s perpetuity, translated and reflected, in Proceedings of Ritsumeikan International Symposium: Stochastic Processes and Applications to Mathematical Finance, edited by J. Akahori, S. Ogawa and S. Watanabe. World Scientific Publishing Co., Singapore (2004) [Google Scholar]
  8. D. Kennedy, Some martingales related to cumulative sum tests and single-server queues. Stoch. Proc. Appl. 4 (1976) 261–269. [Google Scholar]
  9. I. Meilijson, The time to a given drawdown in Brownian motion, in Séminaire de Probabilités XXXVII. Springer (2003) 94–108. [Google Scholar]
  10. Y. Hu, Z. Shi and M. Yor, The maximal drawdown of the Brownian meander. Electron. Commun. Probab. 20 (2015) 1–6. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Mijatović and M.R. Pistorius, On the drawdown of completely asymmetric Levy processes. Stoch. Processes Appl. 122 (2012) 3812–3836. [Google Scholar]
  12. E. Mayerhofer, Three essays on stopping. Risks 7 (2019) 1–10. [Google Scholar]
  13. O. Hadjiliadis and J. Vecer, Drawdowns preceding rallies in the Brownian motion model. Quant. Finance 6 (2006) 403–409. [Google Scholar]
  14. L. Pospisil, J. Vecer and O. Hadjiliadis, Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups. Stoch. Processes Appl. 119 (2009) 2563–2578. [Google Scholar]
  15. L. Pospisil and J. Vecer, Portfolio sensitivity to changes in the maximum and the maximum drawdown. Quant. Finance 10 (2010) 617–627. [Google Scholar]
  16. P. Cheridito, A. Nikeghbali and E. Platen, Processes of class sigma, last passage times, and drawdowns. SIAM J. Financial Math. 3 (2012) 280–303. [Google Scholar]
  17. H. Zhang, Occupation times, drawdowns, and drawups for one-dimensional diffusions. Adv. Appl. Probab 47 (2023) 210–230. [Google Scholar]
  18. P. Gapeev and N. Rodosthenous, On the drawdowns and drawups in diffusion-type models with running maxima and minima. J. math. Anal. Appl. 434 (2016) 413–431. [Google Scholar]
  19. A. Dassios and J.W. Lim, A variation of the Azéma martingale and drawdown options. Math. Finance 29 (2019) 1116–1130. [Google Scholar]
  20. G. Zhang and L. Li, A general method for analysis and valuation of drawdown risk. J. Econ. Dyn. Control 152 (2023). [Google Scholar]
  21. R. Douady, A.N. Shiryaev and M. Yor, On probability characteristics of “downfalls” in a standard Brownian motion. Theory Probab. Appl. 44 (2000) 29–38. [Google Scholar]
  22. M. Magdon-Ismail, A.F. Atiya, A. Pratap and Y.S. Abu-Mostafa, On the maximum drawdown of a Brownian motion. J. Appl. Probab. 41 (2004) 147–161. [Google Scholar]
  23. P. Salminen and P. Vallois, On maximum increase and decrease of Brownian motion. Ann. IHP Probab. Statist. 43 (2007) 655–676. [Google Scholar]
  24. P. Salminen and P. Vallois, On the maximum increase and decrease of one-dimensional diffusions. Stoch. Processes Appl. 130 (2020) 5592–5604. [Google Scholar]
  25. K. Itô and H.P. McKean, Diffusion Processes and Their Sample Paths. Springer Verlag, Berlin, Heidelberg (1974). [Google Scholar]
  26. A.N. Borodin and P. Salminen, Handbook of Brownian Motion – Facts and Formulae, 2nd Edn., 2nd printing. Birkhäuser, Basel, Boston, Berlin (2015). [Google Scholar]
  27. J. Azéma and M. Yor, Une solution simple au probleme de Skorokhod, In Séminaire de Probabilités XIII, Vol. 721 in Springer Lecture Notes in Mathematics, edited by C. Dellacherie, P.A. Meyer and M. Weil. Berlin, Heidelberg, New York (1979) 90–115. [Google Scholar]
  28. J. Azéma and M. Yor, Le probleme de Skorokhod: compléments à léxposé précédent, in Séminaire de Probabilités XIII, Vol. 721, Springer Lecture Notes in Mathematics, edited by C. Dellacherie, P.A. Meyer and M. Weil. Berlin, Heidelberg, New York (1979) 625–633. [Google Scholar]
  29. P.J. Fitzsimmons, Excursions above the minimum for diffusions. arXiv:1308.5189 (2013). [Google Scholar]
  30. J. Pitman and M. Yor, Hitting, occupation and inverse local times of one-dimensional diffusions: martingale and excursion approaches. Bernoulli 9 (2003) 1–24. [Google Scholar]
  31. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd edn. Springer Verlag, Berlin, Heidelberg (2001). [Google Scholar]
  32. B. Maisonneuve, Exit systems. Ann. Probab. 3 (1975) 399–411. [Google Scholar]
  33. L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Vol. 2: Itô Calculus. Cambridge University Press (2000). [Google Scholar]
  34. P. Salminen, P. Vallois and M. Yor, On the excursion theory for linear diffusions. Jap. J. Math. 2 (2007) 97–127. [Google Scholar]
  35. J. Pitman and M. Yor, A decomposition of Bessel bridges. Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 (1992) 425–457. [Google Scholar]
  36. D.A. Darling and A.J.F. Siegert, The first passage problem for a continuous Markov process. Ann. Math. Statist. (1953) 624–639. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.