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Optimal Portfolio Choice in a Jump-Diffusion Model with Self-Exciting
Department of Mathematics, Tongji University, Shanghai, China
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
School of Finance, Shanghai University of Finance and Economics, Shanghai, China
- 1 Department of Mathematics, Tongji University, Shanghai, China
- 2 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
- 3 School of Finance, Shanghai University of Finance and Economics, Shanghai, China
Journal of Mathematical Finance·Volume 09 (2019)·Pages 345–367·Published 19 June 2019·DOI10.4236/jmf.2019.93020
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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.
KeywordsPortfolio ChoiceJump DiffusionStochastic VolatilityHawkes ProcessSelf-Exciting JumpHJB Equation
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