The team Financial and Actuarial Mathematics, Numerical Probability brings together researchers working on probabilistic and statistical modeling in finance, on the mathematical tools and theories relevant in finance, and on numerical methods in probability with main applications in quantitative finance. The current research of the team includes the following topics.

Stochastic optimization, optimal stopping and impulse control, mean-field games and controlled McKean-Vlasov equation, optimal investment in imperfect markets (transaction costs, portfolio constraints), financial risk management (liquidity risk, default risk, execution delay), robust hedging.

Neural network approximation methods for financial and actuarial problems.

Models with jumps and stochastic volatility, regime-switching models, arbitrage, model uncertainty, financial econometrics. Statistics in insurance.

Optimal quantization, probabilistic methods for numerical resolution of nonlinear PDE, Multi-level Monte-Carlo methods, variance reduction, Romberg extrapolation, asymptotic methods in finance, discretization and simulation of Lévy processes.

Backward stochastic differential equations, probabilistic representation of nonlinear PDEs, random matrices, enlargement of filtration, Brownian motion and general theory of processes.

Stochastic algorithms, functional quantization, adaptative discretization, accelerated simulation methods, machine learning.

Statistics of high frequency data, optimal order execution, algorithmic trading, mathematical modeling of limit order book.

Mortality rate modeling, long term interest rate, variable annuities.

Real options, optimal investment in energetic assets (power plants, stockage gas), modeling of electricity prices, strategic interactions in competitive electricity markets.

Counterparty risk in post-crisis markets

CVA, multi-curve term structure models, funding on interest rate derivatives, sovereign risk modeling.

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