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.