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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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