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...ss of F, and therefore, the Martingale Representation Theorem fails. As far as we know, there exists only a very few works addressing the well-posedness of equation (1.1) with the general filtration (=-=[5, 7]-=-). The main idea to study the well-posedness of BSDEs in [5] is as follows. Consider first equation (1.4). Since the filtration F is not equal to the natural one, the following M20,M,F([0, T ];Rn) △ =...

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...µ P t γ||σPt ||2 = −〈σ P t ,Zt〉 ||σPt ||2 , which completes the proof. Proof of Theorem 2.5. The type of FBSDE is in fact a special case of functional differential equations studied by Liang et al in =-=[36]-=- and [37]. We define S([0, T ],Rn), the space of continuous and Ft-adapted processes valued in Rn such that supt∈[0,T ] ∑n i=1 |Sit | ∈ L2(Ω,FT ,Q) and endowed with the norm: ||S||S = EQ { sup t∈[0,T ...

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...nce price as a linear expectation of the payoff plus a pricing premium, where the latter is represented by the solution of a functional differential equation. Such an idea is motivated by Liang et al =-=[29]-=-, where they transform BSDEs to functional differential equations, and solve them on a general filtered probability space. One of the advantages of such a representation is that we only need to solve ...

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...gh this dissertation. Last but not least, I would like to thank my parents for their endless encouragement, support and love. Abstract This thesis is a survey report based on the following two papers =-=[3]-=- and [4]. In [3] a new approach was introduced to interpret backward stochastic differential equations (BSDE) as ordinary functional differential equations on certain path spaces. By Liang, Lyons and ...

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... establish the martingale representation theorem for the martingale parts of (reflecting) symmetric diffusions in a bounded domain with a continuous boundary. Together with an approach put forward in =-=[21]-=-, our martingale representation theorem is then applied to the study of initial and boundary problems for quasilinear parabolic equations by using solutions to backward stochastic differential equatio...