Professor of Operational Research

School of Mathematical Sciences

University of Southampton

Southampton SO17 1BJ

England

**Tel**

+44 (0)23 8059 3657

**Fax**

+44 (0)23 8059 5147

**Email**

**Office Location**

Mathematics Building, Room 10013

**Internal Phone Extension**

23657

**Research Interests**

My recent interest is in optimal decision making problems that involve uncertain data. This 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. Typical examples 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 optimization 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, engineering design etc. I am also interested in risk management models such as condition value at risk models and dominance constrained stochastic program models.

An important component of the
research is to identify uncertainties and quantify them. This is not an easy
task for many so-call data-driven problems where the size of uncertain data
could be small or very large (in which case we will have to be selective). A
popular approach to handle this is distributionally
robust optimization (DRO) which uses partial information to construct a set of
distributions based on empirical data, computer simulation and subjective
judgement and base optimal decision on the worst probability distribution to
mitigate the risk amid incomplete information of uncertainty. Over the past few
years, I have been working on this exciting research area with particular focus
on quantitative stability analysis which quantifies
the difference between the true unknown probability distribution and
approximation based on distributionally robust
approach and its impact on the optimal decision making. I refer interested reader to the website of
workshop at Banff https://www.birs.ca/events/2018/5-day-workshops/18w5102
for an overview of the recent development of DRO.

More recently, I am looking into
so-called preference robust optimization where the underlying uncertainty
arises from decision maker’s utility preferences or risk attitudes. This is a
new stream of research which focuses on endogenous
rather than exogenous uncertainty as in distributionally
robust optimization. It is built on Von Neumann–Morgenstern expected utility theory which
underpins modern economics and stochastic dominance. One of
the main challenges is how to elicit decision maker’s preference either
because there is limited information or the prospect space is too large. There
are also many other challenges such as developing appropriate robust models and
tractable numerical schemes.

**Publications**

**Teaching**

MATH6158 Managing Uncertainty and Risk.

Written by Dr J H Renshaw,