In this paper we analyze a dynamic recursive extension (as developed in Pistorius and Stadje (2017)) of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sharing generalizing classical risk-sharing results for variance through a dynamic inf-convolution problem involving a transformation of the original dynamic deviation measures.
↧