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.
Highlights
Empirical studies suggest that asset price encounters jumps and its volatility is stochastic
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
Summary
Empirical studies suggest that asset price encounters jumps and its volatility is stochastic. [5] solves the optimal investment and consumption problem in a similar model where a state variable (economic factor) is an Ornstein-Uhlenbeck type process of subordinator. [4] solves the portfolio choice problem in a model where volatility is a linear combination of Ornstein-Uhlenbeck type processes of subordinators. Our model has the features of stochastic volatility and self-exciting, while the optimal investment problem is still solvable in sense of by an iteration method, given that the iteration is proved to converge correctly to the unique classical solution of the problem.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call