[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.
