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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-004-0150-7