Hi All,Does anyone know why Ito calculus is used more generally in finance as opposed to Stratonovich?Cheers.

I don't know much about Stratanovich integrals, but if I remember correctly, there is a connection between the two.But I think Stratanovich integrals are not martingales, while Ito integrals are, which gives Ito's integral a serious computational advantage.

In finance, you assume that the observables follows a stochastic process adapted to a fitration F_t. Then you define the (Ito) integral as a limit of sums in a nonanticipatory sense (tha makes sense) and you get the Ito formula.In physics Stratonovich formalism is prefered, in part because the reasoning is the other way around. You have an unknown noise that could be in principle smooth, but much 'faster' than you can measure so that it appears to be stochastic. Assuming a smooth process you take limits and after that, you send your noise to a stochastic process getting Stratonovich. That is, it all depends at which point you introduce a stochastic process as a model of uncertainty, before of after integrating paths.This heuristic reasoning can be found in Bismut's "Mecanique aleatoire", but it is just one of several justifications.Here it is other that a physicist friend of mind told me."If you are physicist and you want your results published, you must use Stratonovich."I suppose it's the same in finance.

This subject was disussed quite a bit years ago, the discretized version of Ito uses left point of the integrand(hence adapted) while Strotonavich uses mid point(hence you have to see the future), thus roughly the popular use of Ito....but when people doing stochastic calculus on manifold, they tend to use Stronavich since it is corordinate invariant.....

QuoteOriginally posted by: madmaxI don't know much about Stratanovich integrals, but if I remember correctly, there is a connection between the two.But I think Stratanovich integrals are not martingales, while Ito integrals are, which gives Ito's integral a serious computational advantage.not only a mere computational advantage - the whole no-arbitrage argument is built on martingales more or less.