Coherent and convex monetary risk measures for unbounded càdlàg processes - Cheridito, Patrick; Delbaen, Freddy; Kupper, Michael (Finance and stochastics, 2005)
This paper studies coherent and convex monetary risk measures on the space of all c`adl`ag processes that are adapted to a given iteration. It shows that if such risk measures are required to be real-valued, then they can only depend on a stochastic process in a way that is uninteresting for many applications. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted c`adl`ag processes that can be extended to coherent or convex monetary risk measures on the space of all adapted c`adl`ag processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded c`adl`ag processes induced by a so called m-stable set.