Minimal supersolutions of convex BSDEs

Abstract

We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.

Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Quadratic BSDEs with convex generators and unbounded terminal conditions
• BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces
• Weak martingale representation for continuous Markov processes and application to quadratic growth BSDEs

Cited by in corpus (3)

• Existence and uniqueness results for BSDEs with jumps: the whole nine yards
• Functional inequalities for forward and backward diffusions
• Hedging under generalized good-deal bounds and model uncertainty