First-order sensitivities of non-Markovian distributionally robust control/stopping problems under L∞ and L2 drift perturbations equal the L1/L2 norms of the Z component of the corresponding (R)BSDE.
Quadratic Mean-Field Reflected BSDEs
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abstract
In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown $z$. Using linearization technique and BMO martingale theory, we first apply fixed point argument to establish uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of a $\theta$-method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the 2nd unknown $z$
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Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs
First-order sensitivities of non-Markovian distributionally robust control/stopping problems under L∞ and L2 drift perturbations equal the L1/L2 norms of the Z component of the corresponding (R)BSDE.