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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE pp 165–188Cite as

Quadratic Backward SDEs

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Part of the book series: Fields Institute Monographs ((FIM,volume 29))

Abstract

In this chapter, we consider an extension of the notion of BSDEs to the case where the dependence of the generator in the variable z has quadratic growth. In the Markovian case, this corresponds to a problem of second-order semilinear PDE with quadratic growth in the gradient term. The first existence and uniqueness result in this context was established by M. Kobylanski in her Ph.D. thesis by adapting some previously established PDE techniques to the non-Markov BSDE framework. In this chapter, we present an alternative argument introduced recently by Tevzadze[39].

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  1. Département de Mathématiques Appliquées, École Polytechnique, Palaiseau Cedex, France

    Nizar Touzi

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  1. Nizar Touzi
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Touzi, N. (2013). Quadratic Backward SDEs. In: Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. Fields Institute Monographs, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4286-8_11

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