2014/09/18 by Bruno Bouchard, Romuald Élie, Bouchard, Bruno +4
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1409.5369
arxiv created 2014/09/18 · openalex publication_date 2014/09/18 · arxiv updated 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the minimal super-solution of a backward stochastic differential equation with constraint on the gains-process. The terminal condition is given by a function of the terminal value of a forward stochastic differential equation. Under boundedness assumptions on the coefficients, we show that the first component of the solution is Lipschitz in space and 1/2-Hölder in time with respect to the initial data of the forward process. Its path is continuous before the time horizon at which its left-limit is given by a face-lifted version of its natural boundary condition. This first component is actually equal to its own face-lift. We only use probabilistic arguments. In particular, our results can be extended to certain non-Markovian settings.