| EPSRC Reference: |
EP/J014427/1 |
| Title: |
On a Robust Approach for Stochastic Equilibrium Problems |
| Principal Investigator: |
Xu, Professor H |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
School of Mathematics |
| Organisation: |
University of Southampton |
| Scheme: |
Standard Research |
| Starts: |
12 May 2012 |
Ends: |
11 November 2013 |
Value (£): |
20,528
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| EPSRC Research Topic Classifications: |
| Mathematical Aspects of OR |
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Summary on Grant Application Form |
Stochastic programming has been extensively used by operation researchers, economists and various decision makers/practitioners to model optimal decision making in economics, management, engineering, transportation networks and the environment. When a decision problem involves not only uncertainty, but also several
decision makers who are in a competitive relationship, it becomes a stochastic game. An important approach in understanding such a game is to look at the equilibrium outcomes. These are the set of possible outcomes at
the end of competition, given that each player seeks to optimize their own payoff.
A fundamental issue in stochastic programming and equilibrium concerns the representation of
uncertainty. Many of the models in the literature assume complete knowledge of the distributions of random variables (representing the uncertainty). In
many practical cases, however, such distributions are not known precisely and have to be either estimated from historical data or constructed using
subjective judgements. The available information is often insufficient to give confidence in the distribution identified. In the absence of full information on the underlying distribution, it may still be possible to
identify a set of possible probability distributions within which the true distribution lies. While a robust optimization approach to this problem is
based on making the decision that would be appropriate given the worst probability distribution in the set of possible distributions, robust analysis of stochastic equilibrium is to look into worst equilibrium outcomes given the incomplete information of the underlying stochastic elements and robust design
requires one to set out optimal policy/parameters which accommodate any worst equilibrium outcomes.
The project is proposed to develop a mathematical framework that allows one to carry out robust anaysis of a stochastic equilibrium problem with incomplete information on the underlying uncertainty, identify optimal policy/design which accommodate the worst possible equilibrium outcomes, develop efficient numerical methods for solving the new mathematical models and apply apply them to some interesting practical problems in economics and engineering with a particular focus on energy industry.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.soton.ac.uk |