  We consider a mean-variance portfolio selection problem in a financial market
with contagion risk. The risky assets follow a jump-diffusion model, in which
jumps are driven by a multivariate Hawkes process with mutual-excitation
effect. The mutual-excitation feature of the Hawkes process captures the
contagion risk in the sense that each price jump of an asset increases the
likelihood of future jumps not only in the same asset but also in other assets.
We apply the stochastic maximum principle, backward stochastic differential
equation theory, and linear-quadratic control technique to solve the problem
and obtain the efficient strategy and efficient frontier in semi-closed form,
subject to a non-local partial differential equation. Numerical examples are
provided to illustrate our results.
