Title: Time Consistency in Multistage Stochastic Optimization
Speaker: Prof. Georg Pflug
Affiliation: Department of Statistics and Operations Research – University of Vienna
Location: CPSE seminar room (C615 Roderic Hill)
Time: 11:00am

Abstract. A fundamental principle for dynamic optimization is Bellman’s priciple, stating that at any initially optimal decision sequence is also optimal at later stages. This time-consistency principle is still valid for stochastic programs if the criterion is to minimze expected costs or to maximize expeted profits. However, as simple examples show, it is not longer valid, if risk-sensitive criteria are chosen such as the optimization of the average value at risk.
It turns out that most risk functionals are time inconsistent, e.g., it may happen that today some loss distribution appears to be less risky than another, but looking at the conditional distribution at a later time, the opposite relation holds. We demonstrate that this time inconsistency disappears if the conditional functionals are defined in an extended manner, i.e., are evaluated under a specific change of measure. It follows from our results that, for consistency reasons, the revelation of partial information in time must dramatically change a decision maker's preferences among the remaining courses of action to keep time consistency.
We extend conditional risk functionals to allow a temporal decomposition of the initial risk functional in time consistent way. With this extension, a Bellmann priciple may be proved. Counterexamples show that without change of measures the only time consistent risk functionals are the expectation and the essential supremum.

About the speaker.

Born on June 10th, 1951 in Vienna. Study of Law, Mathematics and Statistics at the University of Vienna, Magister iuris (1974), Ph.D in Mathematics (1976). Assistant Professor University of Vienna (1976-81). Professor, University of Giessen, Germany (1981-1989). Full Professor, University of Vienna (1989 – ).

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–>Visting Professor at the University of Bayreuth (1979), Michigan State University (1985), University of California Davis (1993), Universite de Rennes (1994), Technion Haifa, Israel (1996), Princeton University (2001), University of California Davis (2006).

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–>Dean, Department of Mathematics, University of Giessen, Germany (1987-88); Dean, Faculty of Business, Economics and Statistics, University of Vienna, Austria (2008-2010); Head, Department of Statistics and Decision Support Systems, University of Vienna (2000-2003); Member of Senate, University of Vienna (200-2003); Research scholar, International Institute of Applied Systems Analysis, IIASA (1990 – ) – Risk, Modelling and Society (RMS), Risk and Vulnerability Project (RAV), .

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Editor in chief: Statistics and Decisions, Central European Journal of Operations Research

Associate editor: Statistics and Probability Letters (1994-2007), Stochastic Programming Electronic Publication Series, Austrian Journal of Statistics, Mathematics of Operations Research (1994 – 1997), Mathematical Methods of OR, Computational Optimization and Applications, Computational Management Science, Energy Systems: Optimization, Modeling, Simulation and Economic Aspects; Vestnik of the Finance Academy, Moscow.

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–>Member, Council of Scientists, INTAS, Bruessel (1999 – 2002); Fellow, International Statistical Institute; Member, executive board of the international committee on stochastic programming; Member, central research council, University of Bolzano/Bozen.

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–>Author Author of 4books, editor of 5 books, and more than 70 publications in refereed journals, such as: Annals of Statistics, Annals of OR, Probability Theory, J Statist. Planning and Inference, J. ACM, Parallel Computing, The Computer Journal, Math. Programming, Mathematics of Optimization, SIAM J. on Optimization, Computational Optimization and Applications, J. Applied Probability, Stoch. Processes and Applications, Graphs and Combinatorics, J. Theoretical Computer Science, Quantitative Finance etc.

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–>Organizer of COMETT II Workshop "Simulation and Optimization", Raach (1992); Workshop"Computer Intensive Methods in Simulation and Optimization", IIASA (1994); EURO Winter School "Stochastic Optimization", Semmering (1996); Fourth World Congress of the Bernoulli Society, Vienna (1996); Workshop Stochastic Dynamic Optimization, IIASA (2002); Workshop series "Mathematical Optimization for Financial Models", Semmering (2003), Cyprus (2003), Bergamo (2004); 11th International Conference on Stochastic Programming, Vienna (2007); APMOD, Vienna and Bratislava (2008).

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–>Project leader of past and present projects: Project leader of past and present projects: Statistical pattern recognition (Austrian National Bank); Pension fund management (BVP pension fund); Data dependency in financial optimization (FWF- Austrian Science Fund); Optimal network design and marketing strategies (Telekom Austria); AURORA-Advanced parallel and distributed algorithms for Computational Finance (FWF); Unit life insurance with guarantee (Austrian National Bank); WEBOPT (European Commission-subproject leader), Risk management in liberalized electricity markets (WWTF); Seeds in Finance (Austrian National Bank), RISKPLAN (Asia-Link), Long-term risk management (FWF), Pension fund management (Bridge Program).