Coherent and convex monetary risk measures for unbounded càdlàg processes

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 ap...

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Published in:	Finance and stochastics Vol. 9; no. 3; pp. 369 - 387
Main Authors:	Cheridito, Patrick, Delbaen, Freddy, Kupper, Michael
Format:	Journal Article
Language:	English
Published:	Heidelberg Springer 01.07.2005 Springer Nature B.V
Subjects:	Capital market Coherence Econometric models Financial economics Finanzmathematik Insurance Mathematics Monetary policy Random variables Risiko Risk Stochastic models Stochastic processes Stochastischer Prozess Studies Theorie Utility functions Switzerland
ISSN:	0949-2984, 1432-1122
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Abstract	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.
AbstractList	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 (-[infinity], [infinity]). The economic interpretation of a value of [infinity] 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. Reprinted by permission of Springer 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.
Author	Cheridito, Patrick Kupper, Michael Delbaen, Freddy
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Snippet	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... 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...
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SubjectTerms	Capital market Coherence Econometric models Financial economics Finanzmathematik Insurance Mathematics Monetary policy Random variables Risiko Risk Stochastic models Stochastic processes Stochastischer Prozess Studies Theorie Utility functions
Title	Coherent and convex monetary risk measures for unbounded càdlàg processes
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