## Financial and Actuarial Mathematics, Numerical Probability: research themes

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 control and applications in finance

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.

### Machine learning and applications in finance and insurance

Neural network approximation methods for financial and actuarial problems.

### Financial and actuarial modeling and statistics

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

### Numerical methods in finance

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.

### Stochastic analysis

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

### Numerical probabilities

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

### Market microstructure and high frequency data

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

### Longevity risk

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

### Energy markets

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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