Coherent and convex risk measures for bounded càdlàg processes

It is common practice to describe the future evolution of a financial profit by a continuous-time stochastic model. A risk measure can then be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions of coherent and convex risk measures to the space of bounded cadlag processes that are adapted to a given filtration. Then, we prove representation results that generalize earlier results for one- and multi-period risk measures, and we discuss some examples.