Hello, would anybody know of any open problems that the industry faces regarding stochastic filtering theory?

Sure, stochastic volatility and more general continuous-time models in financeuse the notion of the instantaneous volatility sigma(t). This notion can be pretty subtle.While sigma(t) can be estimated from option chains, there is also a need to estimate itusing the time and sales series of the underlying security, perhaps supplemented withthe bid-ask series. Using the underlying (as opposed to the option chains) presents 2 filtering problems: What is the best way to estimate sigma(t) if you have underlying (last and/or bid-asks):1. through time t and prior to t.2. both ahead of and behind t. Of course, there is a literature (please google it up yourself) -- however, I am confidentthat any existant estimators can be improved. Also, there are questions of how todefine sigma(t) in a model independent way (what if there are jumps?), and howto construct best estimators both with and without a model, and with and without jumps.Jumps themselves can be tricky to define.

Thanks very much Alan.

You're welcome. Just ran across this paper, which may be of interest:http://arxiv.org/PS_cache/arxiv/pdf/081 ... 3538v4.pdf