FOURTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Carnegie Mellon University
Pittsburgh, PA, USA
July 20-23 2005

WORKSHOP ON FINANCIAL RISK ASSESSMENT

On the morning of Sunday, July 24, there will be a series of presentations and discussions on the topic of Financial Risk Assessment. Attendance will be open and free to those registered to ISIPTA'05.

The talks to be presented at the workshop will be:

• Dynamic monetary risk measures for processes
  Patrick Cheridito
  We study time-consistency properties of processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals.
  Patrick Cheridito's home page.

• Time Consistent and Currency Invariant Convex Risk Measures
  Stephen D'Silva
  In order to study time-consistent monetary concave risk adjusted valuations in a continuous time, finite horizon setting, there arises a need to define risk adjusted valuations at all dates in the time continuum. One approach of tackling this issue is to define risk adjusted valuations at all dates and call this sequence of risk valuations as the risk valuation process. However, monetary risk adjusted valuations enjoy the translation invariance property which enables us to define monetary risk adjusted valuations at intermediate stopping times in terms of the date-0 risk adjusted valuation.
  We characterize these intermediate risk adjusted valuations in terms of the date-0 risk adjusted valuation for strongly relevant time-consistent monetary risk measures. We develop a representation for strongly relevant monetary risk measures which are time consistent at certain specified dates.
  We seek to characterize convex risk measures which are both time consistent and currency invariant. We define currency invariance for monetary concave risk adjusted valuations. We show that only trivial monetary concave risk adjusted valuations satisfy both time consistency and currency invariance for all positive exchange rate processes.

• Generalized Deviation in Risk Analysis
  R. Tyrrell Rockafellar, Stan Uryasev, Michael Zabarankin
  General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their properties are explored with a mind to generating a large assortment of examples and assessing which may exhibit superior behavior. Connections are shown with coherent risk measures in the sense of Artzner, Delbaen, Eber and Heath, when those are applied to the difference between a random variable and its expectation, instead of to the random variable itself. However, the correspondence is only one-to-one when both classes are restricted by properties called lower range dominance, on the one hand, and strict expectation boundedness on the other. Dual characterizations in terms of sets called risk envelopes are fully provided.

  Related Papers:

  • Rockafellar, R. T., Uryasev, S. and M. Zabarankin, Generalized Deviations in Risk Analysis. Finance and Stochastics, Vol. 9, 2005
    Press here to get a pdf file.
  • Rockafellar, R. T., Uryasev, S. and M. Zabarankin, Master Funds in Portfolio Analysis with General Deviation Measures, The Journal of Banking and Finance, Vol. 29, 2005
    Press here to get a pdf file.
  • Rockafellar, R. T., Uryasev, S. and M. Zabarankin, Optimality Conditions in Portfolio Analysis with Generalized Deviation Measures, Mathematical Programming, accepted for publication, 2005
    Press here to get a pdf file.

• Fundamental Theorems of Previsions and Asset Pricing Theories
  Mark Schervish, Teddy Seidenfeld, Jay Kadane
  We explore the connections between the concepts of arbitrage and Dutch Book. These concepts are related to the fundamental theorem of previsions and the fundamental theorem of asset pricing. In loose terms, fair prices for gambles (previsions) are coherent and asset prices are arbitrage free if they are expected values under probability measures. How generally this loose result holds and how closely the two concepts correspond are the main focus of this study.