Article
Licensed
Unlicensed
Requires Authentication
Convex risk measures and the dynamics of their penalty functions
-
Hans Föllmer
Published/Copyright:
September 25, 2009
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
:
Received: 2006-February-16
Accepted: 2006-March-29
Published Online: 2009-09-25
Published in Print: 2006-07
© R. Oldenbourg Verlag, München
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Editorial preface
- Risk measurement with equivalent utility principles
- Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
- On distortion functionals
- Convex risk measures and the dynamics of their penalty functions
- Law invariant convex risk measures for portfolio vectors
- Robust utility maximization in a stochastic factor model
- Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
- On the optimal risk allocation problem
- Monetary utility over coherent risk ratios
- Mean-risk optimization for index tracking
Articles in the same Issue
- Editorial preface
- Risk measurement with equivalent utility principles
- Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
- On distortion functionals
- Convex risk measures and the dynamics of their penalty functions
- Law invariant convex risk measures for portfolio vectors
- Robust utility maximization in a stochastic factor model
- Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
- On the optimal risk allocation problem
- Monetary utility over coherent risk ratios
- Mean-risk optimization for index tracking
