Author(s)

Baojun Bian¹, Xinfu Chen², Xudong Zeng³

¹Department of Mathematics, Tongji University, Shanghai, China.
²Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA.
³School of Finance, Shanghai University of Finance and Economics, Shanghai, China.

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.

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

Bian, B. , Chen, X. and Zeng, X. (2019) Optimal Portfolio Choice in a Jump-Diffusion Model with Self-Exciting. Journal of Mathematical Finance, 9, 345-367. doi: 10.4236/jmf.2019.93020.