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Minimal supersolutions of convex BSDEs. (English) Zbl 1284.60116
Summary: 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.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness
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