Black–Litterman in continuous time: the case for filtering

Abstract

In this article, we extend the Black–Litterman approach to a continuous time setting. We model analyst views jointly with asset prices to estimate the unobservable factors driving asset returns. The key in our approach is that the filtering problem and the stochastic control problem are effectively separable. We use this insight to incorporate analyst views and non-investable assets as observations in our filter even though they are not present in the portfolio optimisation.