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The University of Southampton
Mathematical Sciences

Research Group: Stochastic Programming and Simulation

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Stochastic programing and processes represent an important part of our research. For the optimisation side, our work includes developing and/or investigating new mathematical models which capture the uncertainty and other features such as competition, equilibrium and hierarchical relationships between decision makers. As for the simulation aspect, we work on the construction of stochastic simulation models for the analysis of airline ticket pricing, revenue management models; epidemiological models, especially TB and HIV; healthcare modelling; markov combat models; models of fire service emergency cover.

Stochastic Programming and Simulation
Stochastic Programming

Stochastic Programming

Typical examples that we are interested in are stochastic principal agent models (Stackelberg leader follower models), stochastic Nash equilibrium models, stochastic bilevel programming models, stochastic mathematical programs with equilibrium constraints (SMPEC) models and stochastic equilibrium programs with equilibrium constraints (SEPEC) models. The new stochastic optimisation and equilibrium models have many applications in the study of optimal strategy and competition in energy industry, stability of power system/networks, equilibrium of transportation networks, capacity expansion/investment, optimal policy setting and engineering design. We are also interested in risk management models such as condition value at risk models and dominance constrained stochastic program models.

Design and Analysis of Statistical Simulation Experiments

Design and Analysis of Statistical Simulation Experiments

We work on design of bootstrapping techniques especially suited to the analysis of simulation results, input modelling, such as the use of stochastic mixture models and the estimation of normal-copula models and techniques for improving simulation efficiency and their application in pricing financial derivatives. Though methodological in focus, much of the work has been supported by outside organisations and carried out with their collaboration, e.g., World Health Organisation, National Air Traffic Services, bmi, DSTL, Office of the Deputy Prime Minister (now the Department of Communities and Local Government).

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