Coherent and convex monetary risk measures for unbounded càdlàg processes

Patrick Cheridito (), Freddy Delbaen () and Michael Kupper ()

Finance and Stochastics, 2005, vol. 9, issue 3, 369-387

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 càdlàg 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 $(- \infty, \infty]$ . The economic interpretation of a value of $\infty$ is 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 càdlàg processes that can be extended to coherent or convex monetary risk measures on the space of all adapted càdlàg processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded càdlàg processes induced by a so called m-stable set. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Coherent risk measures; convex monetary risk measures; coherent utility functionals; concave monetary utility functionals; unbounded càdlàg processes; extension of risk measures (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s00780-004-0150-7

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