The Department of Mathematics in Metz, the Institut Elie Cartan de Lorraine (IECL) and the CRAN Nancy are opening a PhD position in mathematics focusing on the mathematics of stochastic games with cyber security applications. The position involves three years of doctoral studies, including potential participation in undergraduate and graduate teaching.

Scientific project description:
Cyber risk is a multidisciplinary subject that requires the use of combined tools from mathematics, computer science, epidemiology and economics. Networks provide a way to model one main difficulty of cyber risk: the fact that the underlying risk consists of many interconnected entities. One objective of this project is the analysis of network topologies on cyber risk management strategies, in particular through prevention and insurance. Networks can be described by associated matrices: one focus of this thesis proposal is the effect of the spectra of these matrices on the cyber risk management policy, in particular in a time-dynamic framework, which gives rise to original stochastic control and differential games problems.

Various guarantees of cyber insurance contracts are currently offered on the insurance and reinsurance markets. The prices of this type of contract are very variable and depend on several macroeconomic factors such as the size of the company, its turnover as well as its exposure to IT risk (typically via the number of computers or servers). However, one aspect that is often ignored is the impact of the graph structure on the safety and robustness of the network.
In this PhD, we aim to contribute to the mathematical characterization of the effect of the underlying network topology on prices, cyber risk assessment and management. To do so, we model the interactions between attackers and defenders as a stochastic game.
Successful applicants will be supervised by Nabil Kazi-Tani, professor at IECL and Vineeth S Varma, CNRS researcher at CRAN.
Please contact professor Nabil Kazi-Tani ( for more information about the position.

Candidate profile:

The candidate should:

  • Hold a master’s degree in applied mathematics: probability/statistics, optimization, graph theory.
  • Have a background in scientific programming (R, Python, Matlab) and be willing to learn cyber security issues.
  • Have English skills allowing scientific written and oral communication.

Application instructions:

All applications must include the following to be considered:

  • Detailed CV
  • Application letter
  • Grade transcripts

Applications must be sent by mail to Nabil Kazi-Tani ( and Vineeth S Varma (

Priority will be given to applications received by October 15, 2022. We will accept applications until the position is filled.

Location :
Institut Elie Cartan de Lorraine (IECL), Université de Lorraine
3 Rue Augustin Fresnel, 57070 Metz
More information about the math institute :