Some results on general quadratic reflected BSDEs driven by a continuous martingale

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We study the well-posedness of general reflected BSDEs driven by a continuous martingale, when the coefficient f of the driver has at most quadratic growth in the control variable Z, with a bounded terminal condition and a lower obstacle which is bounded above. We obtain the basic results in this setting: comparison and uniqueness, existence, stability. For the comparison theorem and the special comparison theorem for reflected BSDEs (which allows one to compare the increasing processes of two solutions), we give intrinsic proofs which do not rely on the comparison theorem for standard BSDEs. This allows to obtain the special comparison theorem under minimal assumptions. We obtain existence by using the fixed point theorem and then a series of perturbations, first in the case where f is Lipschitz in the primary variable Y, and then in the case where f can have slightly-superlinear growth and the case where f is monotonous in Y with arbitrary growth. We also obtain a local Lipschitz estimate in BMO for the martingale part of the solution.
Original languageEnglish
Pages (from-to)1275-1302
Number of pages28
JournalStochastic Processes and their Applications
Issue number3
Early online date8 Nov 2013
Publication statusPublished - Mar 2014


  • Reflected BSDEs
  • Perturbations
  • Continuous-martingale setting
  • BMO
  • Quadratic growth

ASJC Scopus subject areas

  • General Mathematics


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