Hawkes, A.G. (1971) Spectra of Some Self-Exciting and Mutually Exciting Point Processes. Biometrika, 58, 83-90.
https://doi.org/10.1093/biomet/58.1.83

has been cited by the following article:

• TITLE: Optimal Portfolio Choice in a Jump-Diffusion Model with Self-Exciting

  AUTHORS: Baojun Bian, Xinfu Chen, Xudong Zeng

  KEYWORDS: Portfolio Choice, Jump Diffusion, Stochastic Volatility, Hawkes Process, Self-Exciting Jump, HJB Equation

  JOURNAL NAME: Journal of Mathematical Finance, Vol.9 No.3, August 20, 2019

  ABSTRACT: We solve the optimal portfolio choice problem for an investor who can trade a risk-free asset and a risky asset. The investor faces both Brownian and jump risks and the jump is modeled by a Hawkes process so that occurrence of a jump in the risky asset price triggers more sequent jumps. We obtain the optimal portfolio by maximizing expectation of a constant relative risk aversion (CRRA) utility function of terminal wealth. The existence and uniqueness of a classical solution to the associated partial differential equation are proved, and the corresponding verification theorem is provided as well. Based on the theoretical results, we develop a numerical monotonic iteration algorithm and present an illustrative numerical example.