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