Anticipated backward stochastic differential equations
نویسندگان
چکیده
منابع مشابه
Anticipated Backward Stochastic Differential Equations
In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and ...
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In this paper we prove the existence of solutions to 1-dimensional anticipated backward stochastic differential equations with continuous coefficients. We also establish the existence of a minimal solution. Finally we derive a related comparison theorem for these minimal solutions.
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In this paper, after recalling the definition of generalized anticipated backward stochastic differential equations (generalized anticipated BSDEs for short) and the existence and uniqueness theorem for their solutions, we show there is a duality between them and stochastic differential delay equations. We then provide a continuous dependence property for their solutions with respect to the par...
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The BMOmartingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) inRp (p ∈ [1,∞)) and backward stochastic differential equations (BSDEs) in Rp × Hp (p ∈ (1,∞)) and in R∞ × H∞, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman’s inequality plays a crucial role in the development of our theory, wh...
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The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problem...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/08-aop423