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In the academic applied probability/math finance community, Backwards Stochastic Differential Equations (BSDE's) are extremely popular, and they provide a single framework for several different problems, notably hedging and utility maximization, where models of market imperfections might stop older models. The basic setup in a high level sense, is that you specify a terminal condition (i.e. what you might like to hedge at the end of a trading period), and the dynamics in time backwards from that point. For those interested, they are not equivalent to forward SDE's precisely because there is a filtration.

I'd like to know if people are using these devices in practice, and for what purposes, and basically, what is the state of the art?

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Hi here are my two cents,

It is true that BSDE's framework represents a very powerful theoretical tool to attack abstract problems in mathematical finance. Nevertheless to my knowledge they are very rarely used in practice for at least three reasons. First they are very "unnatural" in their expression (integrating in the future in time and still being adapted goes against intuition), second the numerics for BSDE's approximation are not fully mature and even if some algorithms do exist they are exotic and complex so the investments they require is usually considered to big to be worthy, and third there exists for most of real life problems at hand some other solutions that already do the job for the same purpose that BSDE can be used for. So in my opinion unless one can prove a gain of at least a factor of complexity using BSDEs, we will probably never see them used a lot in practice.

Best regards

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