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- Title
Coherent and convex monetary risk measures for unbounded cádlág processes.
- Authors
Cheridito, Patrick; Delbaen, Freddy; Kupper, Michael
- Abstract
Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all cádlág processes that are adapted to a given filtration. We show 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. Therefore, we allow them to take values in. The economic interpretation of a value ofis that the corresponding financial position is so risky that no additional amount of money can make it acceptable. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted cádlág processes that can be extended to coherent or convex monetary risk measures on the space of all adapted cádlág processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded cádlág processes induced by a so called m-stable set.
- Subjects
STOCHASTIC processes; MONEY; MONETARY theory; INSURANCE companies; PROBABILITY theory
- Publication
Finance & Stochastics, 2005, Vol 9, Issue 3, p369
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-004-0150-7