Workshop on RISK MEASURES University of Evry, 6 & 7 July 2006

Abstracts :

Rose Anne Dana, Guillaume Carlier :

> See presentation

Microeconomic problems with concave law invariant utilities. We consider 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 are used. Existence and characterization of solutions are provided. The theory is applied to demand, risk sharing and equilibrium problems. For each of these applications, an example is fully solved.

Fabio Maccheroni :

> See document 1
> See document 2
> See document 3

Dynamic variational preferences monetary utility functions, with Massimo Marinacci, and Aldo Rustichini. We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized, which include the multiplier preferences inspired by robust control and used in macroeconomics, as in a series of paper by Hansen and Sargent, as well as mean-variance preferences of Markovitz and Tobin, used in finance. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in finance and macroeconomic applications. A corollary of our results is that multiplier preferences are time consistent, but mean-variance preferences are not. Our work extends the results obtained by Epstein and Schneider for the multiple priors preferences of Gilboa and Schmeidler. Finally, we show the relation between variational preferences and monetary utility functions.

Stan Uryasev, Professor of University of Florida and Consultant for Standard and Poor's :

> See presentation

Generalized Deviations are Counterparts to Risk Measures Generalized Deviations versus Risk Measures

Coherent Deviations
Portfolio Optimization with Generalized Deviations
Optimal Portfolio Policies with Multiple Deviations
Betas for Optimal Portfolios
Market Equilibrium with Investors Having Different Deviations
Statistics with Generalized Deviations

Michael Kupper, TU Vienna :

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Time-consistency of indifference prices and monetary utility functions. (joint work with Patrick Cheridito, Princeton University). We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that the agent's preferences are given by utility functions, which are updated in a time-consistent way as more information is becoming available. Our main result is that the agent's indifference prices are time-consistent if and only if his preferences can be represented with utility functions that are additive with respect to cash. We call such utility functions monetary. The proof is based on a characterization of time-consistency of dynamic utility functions in terms of indifference sets. As a special case, we obtain the result that expected utility leads to time-consistent indifference prices if and only if it is based on a linear or exponential function.

Michel Crouhy :

Risk Management, Capital Attribution and Performance Measurement in Best Practice Banks

> See presentation

This presentation discusses how risk capital can be attributed to business lines as part of a risk-adjusted performance measurement system. The four different purposes that risk capital does serve are reviewed as well as the measures of risk capital that can accommodate each one of them. Practical issues in implementing a RAROC system are also addressed.

Suzanne Kloeppel :

Dynamic Good Deal Bounds

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In an incomplete market, any arbitrage free price for an untraded payoff cor- responds to its expectation under an equivalent martingale measure. Many of these measures are not very reasonable for pricing because they are too "good" respectively too far away, in an appropriate sense, from the reference measure P. Omitting such measures, we obtain a set Q of pricing measures and a cor- responding price interval which is smaller than the no arbitrage price interval. The lower price bound is minus a coherent risk measure. We study the price bounds as processes. Since their computability and dynamic properties depend on the set Q, the main difficulty is to find an appropriate definition for this set in the dynamic context. In a Lévy setting, we define Q by a pointwise restriction on an appropriate integrand. This allows to apply dynamic programming techniques and yields a nice dynamic behavior of the price bounds. Moreover, we show that the pointwise restriction implies a bound on a more intuitive "global" criterion for too "good" pricing measures.

Lieu : Université d'Evry, Bâtiment des Sciences (Bâtiment Maupertuis)

Accès : Cliquer ici

Accès RER D : station 'Evry Courcouronnes', départs aux 11 et 41 de chaque heure de Paris Gare de Lyon (durée : une demi-heure RER+5min à pieds)

For submissions please contact Stéphane Crépey : stephane.crepey@univ-evry.fr
or
Monique Jeanblanc : monique.jeanblanc@univ-evry.fr