Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition
By Adrien Richou. 2011
66 citations recorded by the source corpus.
Abstract This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on Z that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs.
Subfields: Demography, Finance
View Paper: https://www.semanticscholar.org/paper/63495cd907acf65c95d0292ac565a7d565bd7964
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In Demography
In Finance
- Romuald Elie
- Patrick Cheridito
- Kihun Nam
- P. Briand
- Christian Bender
- Nizar Touzi
- Adrien Richou
- M. Zili
Citations in the corpus
- A simple constructive approach to quadratic BSDEs with or without delay (2013, background): “However, it is possible to solve superquadratic BSDEs when the terminal condition has a special feature: in the markovian case see [19, 16], or when ξ has a bounded Malliavin derivative [8].”
- Numerical simulation of quadratic BSDEs (2013, unknown): “The error is bounded by C p M p for every p > 1; see [28, 40].”
- BSDEs with terminal conditions that have bounded Malliavin derivative (2012, background): “Richou [23] derived the existence of solutions to more general Markovian BSDEs in the case where f and ξ satisfy a local Lipschitz condition with respect to the underlying forward process.”
- 7 – Backward Stochastic Differential Equations (2011, unknown): “Richou [74] derived the existence of solutions to more general Markovian BSDEs in the case where f and ξ satisfy a local Lipschitz condition with respect to the underlying forward process.”