题目：Asset Allocation, Consumption, and Life Insurance Purchase with Stochastic Income in a Contagious Market
In this paper, we consider the optimal asset allocation, consumption, and life insurance purchase strategies for a wage earner with a fixed retirement date under a market with mutual exciting Hawkes jump processes. The Hawkes process captures the impact of contagion that each price jump will influence the probability of the next price jump. The wage earner receives an exogenous stochastic income stream continuously throughout the life. In addition, a lumpsum payment will be paid as a heritage if the wage earner dies before the retirement date. Explicit solutions of the optimal controls are obtained in certain cases by using the dynamic programming principle. For more general cases, we apply the Feynman-Kac formula and develop a numerical scheme. Numerical examples are presented to show that the jump intensities have significant influence on the allocation control but small influence on the consumption and life insurance purchase policies.