Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring

@article{Boyarchenko2022EfficientIZ,
  title={Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring},
  author={Svetlana Boyarchenko and Sergei Levendorskii},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.02858}
}
. We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse Z -transform, the Fourier/Laplace inversion and Wiener-Hopf factorization, and discuss efficient numerical methods for realization of these formulas. As applications, the cumulative probability distribution function of the process and its running maximum and the price of the option to exchange the power of a stock… 

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