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Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
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Guillaume Carlier
Published/Copyright:
September 25, 2009
SUMMARY
This paper considers a class of one dimensional calculus of variations problems with monotonicity and comonotonicity constraints arising in economic and financial models where law invariant concave criteria (or law invariant convex measures of risk) are used. Existence solutions, optimality conditions, sufficient conditions for the regularity of solutions are established. Applications to risk sharing with convex comonotone law invariant risk measures or with robust utilities are given.
Key words and phrases: law invariant utility functions; monotonicity and comonotonicity; risk-sharing; constrained dynamic optimization
:
Received: 2005-December-08
Accepted: 2006-March-20
Published Online: 2009-09-25
Published in Print: 2006-07
© R. Oldenbourg Verlag, München
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- Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
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- Convex risk measures and the dynamics of their penalty functions
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- 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
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Keywords for this article
law invariant utility functions;
monotonicity and comonotonicity;
risk-sharing;
constrained dynamic optimization
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
