A stability approach for solving multidimensional quadratic BSDES

Jonathan Harter · Adrien Richou

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Fuzzy Systems and Optimization

Abstract

We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is characterized by constraints on some uniform a priori estimate on solutions of a sequence of approximated BSDEs. We also present effective examples of applications. Our approach relies on the strategy developed by Briand and Elie in [Stochastic Process. Appl. 123 2921–2939] concerning scalar quadratic BSDEs.

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References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2000Backward stochastic differential equations and partial differential equations with quadratic growth 1994Continuous Exponential Martingales and BMO 1989Stochastic Calculus in Manifolds 2006BSDE with quadratic growth and unbounded terminal value 2003BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations 2007Solvability of backward stochastic differential equations with quadratic growth

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