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...

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first...