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SUMMARY
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.
Key words and phrases: dynamic convex risk measures; conditional risk measures; robust representation; dynamic penalty functions; time-consistency; asymptotic safety; asymptotic precision; entropic risk measure
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Received: 2006-February-16
Accepted: 2006-March-29
Published Online: 2009-09-25
Published in Print: 2006-07
© R. Oldenbourg Verlag, München
