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

Yingming Ge () and Lingfei Li
Additional contact information
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)

International Journal of Financial Engineering (IJFE), 2020, vol. 07, issue 04, 1-46

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.

Keywords: Hilbert transform; sinc expansion; stochastic control; piecewise constant policy approximation; jump-diffusions; option pricing; optimal investment (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S2424786320500279
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijfexx:v:07:y:2020:i:04:n:s2424786320500279

Ordering information: This journal article can be ordered from

DOI: 10.1142/S2424786320500279

Access Statistics for this article

International Journal of Financial Engineering (IJFE) is currently edited by George Yuan

More articles in International Journal of Financial Engineering (IJFE) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().