Convex risk measures and the dynamics of their penalty functions

Föllmer Hans and Penner Irina

Statistics & Risk Modeling, 2006, vol. 24, issue 1, 61-96

Abstract: We study various properties of a dynamic convex risk measure for bounded random variables which describe the discounted terminal values of financial positions. In particular we characterize time-consistency by a joint supermartingale property of the risk measure and its penalty function. Moreover we discuss the limit behavior of the risk measure in terms of asymptotic safety and of asymptotic precision, a property which may be viewed as a non-linear analogue of martingale convergence. These results are illustrated by the entropic dynamic risk measure.

Keywords: dynamic convex risk measures; conditional risk measures; robust representation; dynamic penalty functions; time-consistency; asymptotic safety; asymptotic precision; entropic risk measure (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:24:y:2006:i:1:p:61-96:n:3

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DOI: 10.1524/stnd.2006.24.1.61

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