Backward SDEs with Superquadratic Growth

In this paper, we discuss the solvability of backward stochastic differential equations(BSDEs) with superquadratic generators. We first prove that given a superquadraticgenerator, there exists a bounded terminal value, such that the associated BSDEdoes not admit any bounded solution. On the other hand, we prove that if thesuperquadratic BSDE admits a bounded solution, then there exist infinitely manybounded solutions for this BSDE.[...]

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Year of publication:	2009-02-19
Authors:	Delbaen, Freddy ; Hu, Ying ; Bao, Xiaobo
Institutions:	National Centre of Competence in ResearchFinancial Valuation and Risk Management
Subject:	Markov-Modell \| Markov Models \| Wachstum \| Stochastische Differentialgleichung \| A-priori-Abschätzung \| estimate

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1 Introduction
2 Dynamic Utility Functions and Backward SDEs.
3 Backward SDEs with superquadratic growth.
3.1 Non-existence of the solution
3.2 Non-uniqueness of the Solution
3.3 Non-stability of the solutions
3.4 A solution to BSDE (g, v)
4 Existence of solution to BSDEs in the Markoviancase
4.1 Lipschitz case
4.2 A Priori estimates of Z
4.3 Lower semi-continuous case
4.4 Bounded and Continuous Case
References

Persistent link: https://www.econbiz.de/10005868777