Applications of forward-backward stochastic differential equations to financial modelling

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In financial modelling it is assumed that the only information which can be used in decision making is present and past information. Otherwise, investors would be able to make riskless profits with positive probability. Mathematical models of financial markets are usually considered ill-posed if they allow for riskless profits with positive probability. Nevertheless, we recognize that some information about the future behaviour of certain derivative security prices is available to all market participants and must be regarded as a piece of current information. The simplest example is that the redemption value of a bond is known at issue.