Arnaud Lionnet

Interests

• Probability, statistics and analysis :
  • Backward stochastic differential equations (BSDEs).
• Numerical methods :
  • Probabilistic numerical methods for parabolic PDEs (in particular via forward-backward SDEs),
  • Numerical methods for BSDEs with monotone drivers of polynomial growth.
• Mathematical finance and economics :
  • Risk management of financial derivatives (pricing and hedging),
  • Systems of interacting agents,
  • Systemic risk.

My research is concerned mainly with the mathematics of the modeling and the decision-making problems which arise in finance and economics.

One such problem is the risk-management of derivatives products by the Quants in investment banks. It leads to solving parabolic PDEs or, equivalently but more generally, systems of forward and backward SDEs. In parallel with the questions of well-posedness of these equations, one must seek for methods to solve them numerically.

Another topic I am interested in is the modeling of systems of economic agents, when they are not isolated and making decisions individually in face of uncertainty about the future, but form a system of interacting agents. I am particularly interested in systemic risk, where the agents are financial institutions that borrow from and lend to each other.

Publications and working papers

1. A. Lionnet, G. dos Reis and L. Szpruch, Full-Projection scheme for monotone BSDEs with polynomial growth.
   To be submitted, 2016+ (18 pages). On arXiv.
2. A. Lionnet, Adapted time steps explicit scheme for monotone BSDEs.
   Submitted, 2016+ (31 pages). On arXiv.
3. J. Bielagk, A. Lionnet and G. dos Reis, Equilibrium pricing under relative-performance concerns.
   SIAM Journal on Financial Mathematics (to appear), 2015+ (45 pages). On arXiv.
4. A. Lionnet, G. dos Reis and L. Szpruch, Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth.
   In revision, 2016+ (49 pages). On arXiv. Supplementary notes.
5. A. Lionnet, On BSDEs up to an unbounded stopping time.
   Work in progress.
6. A. Lionnet, G. dos Reis and L. Szpruch, Time discretization of FBSDEs with polynomial growth drivers and reaction-diffusion PDEs.
   Annals of Applied Probability, 2015 (63 pages). On arXiv.
7. A. Lionnet, Some results on general quadratic reflected BSDEs driven by a continuous martingale.
   Stochastic Processes and their Applications, 2014 (28 pages). On arXiv. Also in the journal (gold open access paid for by RCUK).
8. G. Liang, A. Lionnet and Z. Qian, On Girsanov's tranform for BSDEs.
   In revision. On arXiv.

Funding, grants, awards, etc

Funding obtained for my research projects :

• Fondation Mathématique Jacques Hadamard, Postdoctoral Fellowship.
• London Mathematical Society, 150th Anniversary Postdoctoral Mobility Grant.

Funding obtained during my studies :

• Ecole Normale Supérieure de Lyon, stipendiary student.
• Lamb and Flag Scholar of St John's College, Oxford (funded by the profits made in the Lamb and Flag pub).

I also received funding from the UK's Engineering and Physical Sciences Research Council (grant EP/P505216/1), from the Oxford-Man Institute through their Student Scholarships, and from the Oxford Mathematical Institute Prizes Fund.