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  Dynamic Pricing and Learning

   Faculty of Social Sciences

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  Dr Athanasios Avramidis  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

Main research aims. This project is on dynamic pricing and learning: statistical learning combined with price optimization. The precise content will depend on a survey of key literature and the strengths and interest of the research team.

Main techniques to be used. Typically a stochastic process describing the demand is, or must be, learned (estimated) via price experimentation [Besbes and Zeevi 2009, den Boer and Zwart 2015]; this learning typically involves some cost. There arises an exploration-exploitation tradeoff similar to that in the stochastic multi-armed bandit literature [Lai and Robbins 1985, Burnetas and Katehakis 1996, Cappe et al 2015a,b]. The research aims to price and learn so as to minimize the regret (gap to the optimum). Large-deviation (`concentration') techniques are essential.

Research importance. This area regularly attracts the interest of prominent, respected researchers. Results eventually find application in many industries (travel, hospitality, retail).

Possible post-PhD opportunities. A strong PhD (evidenced by journal publications) would provide solid foundation towards a career in academia or industry. A typical post-PhD position would be a post-doctoral researcher; lecturer (assistant professor); or data scientist.

Candidate description. A good candidate will have a first-class degree in a quantitative discipline (Mathematics, Computer Science, Engineering); interest in mathematically rigorous research (developing new theory via mathematical proof), and in computation. A very strong candidate will have substantial background in probability and mathematical statistics; the ability to study independently and to self-guide the research when the need or opportunity arises. Ambition to pursue an academic career is another plus.

Primary supervisor. Athanassios (Thanos) N. Avramidis; for research publications, see or

Host Institution

You will be based at the University of Southampton, a research intensive university and a founding member of the Russell Group of elite British universities. In the 2014 Research Excellence Framework, Southampton was ranked 8th for research intensity. In 2017-18, Southampton has been ranked 5th in the UK for research grant income. Besides being recognised as one of the leading research universities in the UK, Southampton has also achieved consistently high scores for its teaching and learning activities. In the Research Excellence framework, 100% of Mathematics research impact and research environment was specifically rated as of internationally excellent or world-leading quality. The broad range of Mathematical Sciences at Southampton gives Southampton a unique ability to contribute to the scientific and social challenges facing society.

Southampton has an excellent track record for optimisation. Statistics and Operational Research groups have existed within Mathematical Sciences since the 1960s. In the early 2000s, the broad multidisciplinary nature of Southampton activity in these areas was recognised through the establishment of the Centre of Operational Research, Management Sciences and Information Systems CORMSIS, which spans Mathematical Sciences and Southampton Business School. Operational Research at the University of Southampton is ranked 33th in the world, and 7th in the UK, according to the latest QS World Rankings. You will be a member of CORMSIS for the duration of your PhD studies.

Entry Requirements

A very good undergraduate degree (at least a UK 2:1 honours degree, or its international equivalent).

How To Apply

Apply for the research degree programme PhD Mathematical Sciences in the Faculty of Social Sciences.

Applications should be made online.

Applications should include:

Research Proposal

Curriculum Vitae

Two reference letters

Degree Transcripts to date

Apply online:

Computer Science (8) Mathematics (25)

Funding Notes

For UK students, Tuition Fees and a stipend of £15,285 tax-free per annum for up to 3.5 years.


Besbes, O. and Zeevi, A., ``Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms'', Operations Research, Vol. 57, No. 6, 2009, pp. 1407--1420.
Burnetas, A. N. and M. N. Katehakis, ``Optimal Adaptive Policies for Sequential Allocation Problems'', Advances in Applied Mathematics, Vol. 17, 1996, pp. 122--142.
Cappe, 0, Garivier, A, Maillard, O.-A., Munos, R, and Stoltz, G. ``Kullback-Leibler upper confidence bounds for optimal sequential allocation'', The Annals of Statistics, Vol. 41, No. 3, 2021, pp. 1516--1541.
Dembo, A. and O. Zeitouni, ``Large Deviation Techniques and Applications'', Springer, 1998.
den Boer, A. V. and B. Zwart, ``Dynamic pricing and learning with finite inventories'', Operations Research, Vol. 63, No. 4, 2015, pp. 965--978.
Lai, T. L. and H. Robbins, ``Asymptotically efficient adaptive allocation rules'', Advances in Applied Mathematics, Vol. 6, 1985, pp. 4--22.