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[00663] Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its proof of overcoming the curse of dimensionality

  • Session Time & Room : 1E (Aug.21, 17:40-19:20) @E704
  • Type : Contributed Talk
  • Abstract : In this talk, we first provide a brief introduction to quantum computing from a mathematical perspective. No prior knowledge of quantum computing is necessary. We then introduce a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension d of the PDE and the reciprocal of the prescribed accuracy ε and so demonstrate that our quantum Monte Carlo algorithm does not suffer from the curse of dimensionality. This talk is based on a joint work with Yongming Li.
  • Classification : 65M75, 91G20, Deep Learning method for nonlinear PDEs
  • Format : Talk at Waseda University
  • Author(s) :
    • Ariel Neufeld (NTU Singapore)
    • Philipp Schmocker (NTU Singapore)
    • Sizhou Wu (NTU Singapore)