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Stochastics, Optimization, and Algorithms

Statistical Methods

  • High-frequency factor modeling

  • State-varying factor models of large dimension

  • Robust large-dimensional factor modeling

  • Regularized principal component analysis

  • Inference for point processes and jump-diffusions

  • Risk measure estimation

  • Affine modeling calibration theory

Monte Carlo Simulation

  • Efficient rare-event algorithms

  • Exact sampling schemes for stochastic differential equations

  • Discretization methods

  • Sampling algorithms for point processes

  • Multi-level methods 

Optimization

  • Large-Scale Optimization

  • Stochastic Programming

  • Optimization tools for machine learning

  • Numerical optimization methods

  • Warm starting approaches

High Performance Computing

  • Parallel structures

  • GPU computing

  • Quantum computing