Solvability of backward stochastic differential equations with quadratic growth

By Revaz Tevzadze. 2007

211 citations recorded by the source corpus.

We prove the existence of the unique solution of a general backward stochastic differential equation with quadratic growth driven by martingales. A kind of comparison theorem is also proved.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/69e4bd323203c2f5ec8e155251b2c677714ea114

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In Applied Mathematics

In Control and Systems Engineering

In Finance

Citations in the corpus

7 – Backward Stochastic Differential Equations (2011, unknown): “Tevzadze [80] proved the well-posedness for multidimensional quadratic BSDE in the case where the terminal condition has a small enough L∞-norm.”
ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL (2015, background): “However, with a generator of quadratic growth, such a property was shown by Tevzadze (2008) only if Assumption 2.3(v) holds (see proposition 2), or if the terminal condition and F̂0 are small enough and if Assumption 2.4(v) holds (see proposition 1).”
Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators (2014, unknown): “[11] R. Tevzadze, Solvability of backward stochastic differential equations with quadratic growth, Stoch.”
A financial market with interacting investors: does an equilibrium exist? (2011, methodology): “While Kobylanski’s proof cannot be generalized to n > 1, Tevzadze [20] presents an alternative derivation of Kobylanski’s results via a fix point argument.”
A simple constructive approach to quadratic BSDEs with or without delay (2013, methodology): “In the Lipschitz-quadratic case, Tevzadze [14] obtained via a Picard iteration argument, the existence of a unique solution to quadratic scalar BSDEs, which remarkably extends to multidimensional Y components for small terminal conditions.”
Multidimensional quadratic and subquadratic BSDEs with special structure (2013, background): “Tevzadze [19] gave an existence and uniqueness result for multidimensional BSDEs with general drivers of quadratic z-growth in the case where the terminal condition has small L1-norm.”
Quadratic BSDEs with convex generators and unbounded terminal conditions (2007, methodology): “[39] Tevzadze, R. (2008) Solvability of backward stochastic differential equations with quadratic growth.”
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition (2011, unknown): “Let us remark that this result has been revisited recently thanks to a fixed point argument by Tevzadze in [28].”
Numerical simulation of quadratic BSDEs (2013, unknown): “When the terminal condition is bounded, we refer to [7, 34, 35, 42], and, in the unbounded case, we refer to [3, 8, 9, 19, 20].”
Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, background): “Some other authors have obtained further results in some particular situations (see for instance Hu & Schweizer [28], Hu, Imkeller & Muller[27], Mania and Tevzadze [36] or Delbaen, Hu & Richou [13]).”
A class of globally solvable Markovian quadratic BSDE systems and applications (2016, methodology): “The uniqueness part of the proof is based on a result [Fre14, Proposition 2.1] of Frei, which, in turn extends [Tev08, Proposition 1] from BSDE whose generator does not depend on y and the terminal condition is small in L ∞ -norm, to those whose terminal condition is small in the BMO-norm (see,…”