A NOTE ON COMONOTONICITY AND POSITIVITY OF THE CONTROL COMPONENTS OF DECOUPLED QUADRATIC FBSDE

Goncalo Dos Reis, Ricardo J. N. Dos Reis

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Abstract

In this note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a by-product one obtains conditions that allow establishing the positivity of the control process.

Original languageEnglish
Article number1350005
Number of pages11
JournalStochastics and dynamics
Volume13
Issue number4
DOIs
Publication statusPublished - Dec 2013

Keywords

  • BSDE
  • forward-backward SDE
  • quadratic growth
  • comparison
  • positivity
  • stochastic calculus of variations
  • Malliavin calculus
  • Feynman-Kac formula
  • GROWTH
  • BSDES

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