Article2014

Minimal supersolutions of BSDEs with lower semicontinuous generators

Gregor Heyne · Michael Kupper · Christoph Mainberger

22 citations0/0 files storedAnnales de l Institut Henri Poincaré Probabilités et Statistiques

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

Abstract

Nous étudions des sur-solutions minimales d’équations stochastiques rétrogrades. Nous montrons l’existence et l’unicité de telles sur-solutions minimales lorsque le générateur est conjointement semi-continu inférieurement, minoré par une fonction affine de la variable de contrôle et satisfait une condition spécifique de normalisation. Le résultat principal est obtenu en utilisant une convergence de semi-martingales.

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References

2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 2005Stochastic Integration and Differential Equations 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 2008Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation 1999Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type

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2016A general Doob-Meyer-Mertens decomposition for g-supermartingale systems 2017One dimensional BSDEs with logarithmic growth application to PDEs

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