Before revision:  Anal. 256 (2009) 3996-4029} (briefly,the FKV paper), where they made some important contributions to the subject and presented some good ideas of financial applications. Unfortunately, there are serious shortcomings in the FKV paper. First, most of the principal results in the FKV paper were based on the premise that the locally L ^{0}--convex topology for every locally L ^{0--conditional risk measure (1\leq p\leq+\infty) can be uniquely extended to an L^{0}} --convex module may be induced by a family of L^{0 the FKV paper ever gave a proof of this premise, but there was a hole in this proof, in fact, it remains open up to now whether the premise is valid or not.
After revision:  Anal. 256 (2009) 3996-4029} conditional risk measures to prove that every L ^{0}--convex topology for every locally L ^{0--conditional risk measure (1\leq p\leq+\infty) can be uniquely extended to an L^{0}} --convex module may be induced by a family of L^{0 the FKV paper ever gave a proof of this premise, but there was a hole in this proof, in fact, it remains open up to now whether the premise is valid or not.