Risk measures and capital requirements for processes

In this paper we propose a generalization of the concepts of convex and coherent risk measures to a multi-period setting, in which payoffs are spread over different dates. To this end, a careful examination of the axiom of translation invariance and the related concept of capital requirement in the one-period model is performed. These two issues are then suitably extended to the multi-period case, in a way that makes their operative financial meaning clear. A characterization in terms of expected values is derived for this class of risk measures and some examples are presented.