Emerging Research Fronts Comments by Wlodzimierz Ogryczak

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ESI Special Topics, June 2004
Citing URL: http://www.esi-topics.com/erf/2004/june04-WlodzimierzOgryczak.html

From •>>June 2004

Wlodzimierz Ogryczak answers a few questions about this month's emerging research front in field of Mathematics:

Mathematics
Article: Dual stochastic dominance and related mean-risk models
Authors: Ogryczak, W;Ruszczynski, A
Journal: SIAM J OPTIMIZATION, 13: (1) 60-78, SEP 5 2002
Addresses:
Warsaw Univ Technol, Inst Control & Computat Engn, PL-00665 Warsaw, Poland.
Warsaw Univ Technol, Inst Control & Computat Engn, PL-00665 Warsaw, Poland.
Rutgers State Univ, Dept Management Sci & Informat Syst, Piscataway, NJ 08854 USA.
Rutgers State Univ, RUTCOR, Piscataway, NJ 08854 USA.

  Why do you think your paper is highly cited?

“The SSD relation depends on comparison of multiple criteria defined as expected shortages of outcomes to various target values.”

Quantile risk measures have recently been widely recognized by both researchers and practitioners in decision-making under risk. Our paper definitely resolves the problem of quantile characteristics of the stochastic dominance by relating it to the standard duality theory in convex analysis.

  Does it describe a new discovery or new methodology that's useful to others?

The key discovery is that by exploiting duality relations of convex analysis we can develop the quantile model of stochastic dominance for general distributions. This allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation. Thus, the paper presents a new methodology as well as identifies new relations between existing approaches.

  How did you become involved in this research?

I was involved in the research on equity (fairness) among outcomes in Multiple Criteria Optimization. Andrzej Ruszczynski was strongly involved in Stochastic Optimization. When we met in the International Institute for Applied Systems Analysis we realized that we were dealing with similar problems although in different environments. The relation of stochastic dominance, and specifically its dual model, turned out to be a common factor in both our problems.

  Could you summarize the significance of your paper in layman's terms?

Several decisions results can be evaluated only from the perspective of uncertain future outcomes. Therefore, comparing uncertain outcomes is one of the fundamental interests of decision theory. The second degree stochastic dominance (SSD relation) is crucial for decision-making under risk. An SSD dominating outcome is preferred within all risk-averse preference models where larger outcomes are preferred. It is therefore a matter of primary importance that a decision model be consistent with the SSD relation. The SSD relation depends on comparison of multiple criteria defined as expected shortages of outcomes to various target values. In several applications it is much more convenient to deal with outcome characteristics defined as means within specific percentages (quantiles) of the worst outcomes. We have proven by the standard duality theory that, indeed, comparison of such quantile characteristics represents a dominance relation equivalent to the SSD. This allows us to show that several decision models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation.

Professor Wlodzimierz Ogryczak
Head of Optimization and Decision Support Division
Institute of Control and Computation Engineering
Warsaw University of Technology
Warsaw, Poland

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ESI Special Topics, June 2004
Citing URL: http://www.esi-topics.com/erf/2004/june04-WlodzimierzOgryczak.html