BSDEs with terminal conditions that have bounded Malliavin derivative

By Patrick Cheridito, Kihun Nam. 2012

59 citations recorded by the source corpus.

Abstract We show existence and uniqueness of solutions to BSDEs of the form Y t = ξ + ∫ t T f ( s , Y s , Z s ) d s − ∫ t T Z s d W s in the case where the terminal condition ξ has bounded Malliavin derivative. The driver f ( s , y , z ) is assumed to be Lipschitz continuous in y but only locally Lipschitz continuous in z. In particular, it can grow arbitrarily fast in z. If in addition to having bounded Malliavin derivative, ξ is bounded, the driver needs only be locally Lipschitz continuous in y. In the special case where the BSDE is Markovian, we obtain existence and uniqueness results for semilinear parabolic PDEs with non-Lipschitz nonlinearities. We discuss the case where there is no lateral boundary as well as lateral boundary conditions of Dirichlet and Neumann type.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/161aca7f1ae768ef9168a5d0e1dd05bde65d11a5

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Citations in the corpus

A class of globally solvable Markovian quadratic BSDE systems and applications (2016, background): “6 It is known then (see [BE13] and [CN14] for sufﬁcient conditions on X, f j and g j ) that the j -th component Z j of the solution is bounded, too.”
Multidimensional quadratic and subquadratic BSDEs with special structure (2013, background): “Moreover, if j has bounded Malliavin derivative, the growth of f ðs; y; zÞ in z can be arbitrary; see [5].”
7 – Backward Stochastic Differential Equations (2011, unknown): “When d = 1, PDEBSDE relationships are generalized in the recent paper by Cheridito and Nam [17] and will be presented in Section 4.”