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Stochastics, Optimization, and Algorithms

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Statistical Methods


  • Regularized principal component analysis
  • Inference for point processes and¬†jump-diffusion
  • Risk measure estimation
  • Affine modeling calibration theory
  • Robust large-dimensional factor modeling State-varying factor models of large dimension
  • High-frequency factor modeling

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


  • Stochastic Programming
  • Optimization tools for machine learning
  • Numerical optimization methods
  • Warm starting approaches

High Performance Computing


  • Parallel structures
  • GPU computing
  • Quantum computing