Dynamic risk measures with markets volatility
In this paper, we extend to a special position space the convex risk measures introduced in F¨ollmer and Schied [12] and the dynamic convex risk measures introduced in Detlefsen and Scandolo [10]. Since the risk in ﬁnancial markets has become much more uncertain and volatile, we consider the risk measures on a special space L p ( · ) , where the variable exponent p ( · ) is no longer a given real number, as in the space L p , but a random variable, which reﬂects the possible volatility of the ﬁnancial markets. By further developing the axioms related to this class of risk measures, we are able to derive dual representation for them.