BSDE with quadratic growth and unbounded terminal value

By P. Briand, Ying Hu. 2005

380 citations recorded by the source corpus.

In this paper, we study the existence of solution to BSDE with quadratic growth and unbounded terminal value. The main idea consists in using a localization procedure together with a priori bounds.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/47100f8de8ff6f3d06d0eca5ba3fc7e2a97f656a

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Harmonic analysis of stochastic equations and backward stochastic differential equations (2008, result): “Later, such kind of results are widely obtained and used, among others, by Hu, Imkeller, and Müller [26], Hu and Zhou [28], Barrieu and El Karoui [2], Briand and Hu [6, 7], and Hu et al.”
Numerical simulation of BSDEs with drivers of quadratic growth (2010, background): “Many papers deal with existence and uniqueness of solution for such BSDEs: we refe r the reader to [17, 18] when the terminal condition is bounded and [3, 4, 9] for the unbounded case.”
BSDEs with terminal conditions that have bounded Malliavin derivative (2012, background): “ion in the case where f does not grow faster than quadratically in z and ξ is bounded. BSDEs with drivers of quadratic growth in z and unbounded terminal conditions have been studied by Briand and Hu [4, 5] as well as Delbaen et al. [9]. Delbaen et al. [8] showed that if the driver f only depends on”
A Stochastic Control Approach to a Robust Utility Maximization Problem (2007, background): “A class of BSDEs with quadratic growth and unbounded terminal value has recently been studied in [3], but (38) does not satisfy the assumptions of that paper as soon as ρ is unbounded.”
On well-posedness of forward-backward SDEs-A unified approach (2011, background): “, [9], [2]), the following special cases of (3.”
A class of globally solvable Markovian quadratic BSDE systems and applications (2016, neutral): “7) can also be established using a localization technique of [12] or from a forward point of view, as in [5], as follows.”
On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions (2009, methodology): “As in part 5 of [3], this assumption allows us to reduce hypot hesis of [4].”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “The existence for unbounded ξ was solved only very recently by Briand and Hu (2006).”
7 – Backward Stochastic Differential Equations (2011, neutral): “BSDEs with drivers of quadratic growth in z and unbounded terminal conditions have been studied by Briand and Hu [12, 13] as well as Delbaen et al.”
A simple constructive approach to quadratic BSDEs with or without delay (2013, background): “Once again we derive this classical upper bound (see [11] or [4]) with simple arguments.”
BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces (2007, background): “Such quadratic BSDEs have been intensively studied by Kobylanski [14] and then by Lepeltier and San Martı́n in [15]; we refer the reader to [4] for the case of an unbounded terminal condition.”
A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem (2010, methodology): “This is done by using the same methodology as in [ BH06 ]: this step allows to prove existence for solutions of the BSDE with generator f when the terminal condition is arbitrary and bounded.”
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, background): “uadratic BSDE Yt = ξ + ZT t |Zs| 2 ds − ZT t ZsdWs, we ﬁnd the explicit solution Yt = log E eξ|F t and we immediatelysee that we just need to have an exponential moment for ξ to obtain a solution. In [5], Briand and Hu show an existence result for quadratic BSDEs when the terminal condition has such”
Optimal consumption and investment in incomplete markets with general constraints (2010, background): “results from Kobylanski [9] and Morlais [10] on the existence and properties of solutions to BSDEs with drivers of quadratic growth (for extensions to unbounded terminal conditions, see Briand and Hu [2, 3], Ankirchner et al. [1] as well as Delbaen et al. [5]). Thestructureof the paperis as follows:”
Quadratic BSDEs with convex generators and unbounded terminal conditions (2007, background): “In order to carry out the purpose, we firstly establish a priori estimate on exponential moments of the term Y of G-BSDE (2) as in [3] or [10].”