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A Hilbert transform approach for controlled jump-diffusions with financial applications

Author

Listed:
  • Yingming Ge

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong (SAR))

  • Lingfei Li

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong (SAR))

Abstract

We propose a new computational method for a class of controlled jump-diffusions for financial applications. In the first step of our method, we apply piecewise constant policy approximation where we partition the time horizon into small time intervals and the control is constant on each interval. In the second step, we develop a Hilbert transform approach to solve a discrete time dynamic programming problem. We provide rigorous error bounds for the piecewise constant policy approximation for controlled jump-diffusions, generalizing previous results for diffusions. We also apply our method to solve two classical types of financial problems: option pricing under uncertain volatility and/or correlation models and optimal investment, including utility maximization and mean-variance portfolio selection. Through various numerical examples, we demonstrate the properties of our method and show that it is a computationally efficient choice for low-dimensional problems. Our method also compares favorably with some popular approaches.

Suggested Citation

  • Yingming Ge & Lingfei Li, 2020. "A Hilbert transform approach for controlled jump-diffusions with financial applications," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 1-46, December.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:04:n:s2424786320500279
    DOI: 10.1142/S2424786320500279
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    Cited by:

    1. Jie Chen & Liaoyuan Fan & Lingfei Li & Gongqiu Zhang, 2022. "A multidimensional Hilbert transform approach for barrier option pricing and survival probability calculation," Review of Derivatives Research, Springer, vol. 25(2), pages 189-232, July.

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