Household lifetime strategies under a self-contagious market

Guo Liu, Zhuo Jin*, Shuanming Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper, we consider the optimal strategies in asset allocation, consumption, and life insurance for a household with an exogenous stochastic income under a self-contagious market which is modeled by bivariate self-exciting Hawkes jump processes. By using the Hawkes process, jump intensities of the risky asset depend on the history path of that asset. In addition to the financial risk, the household is also subject to an uncertain lifetime and a fixed retirement date. A lump-sum payment will be paid as a heritage, if the wage earner dies before the retirement date. Under the dynamic programming principle, explicit solutions of the optimal controls are obtained when asset prices follow special jump distributions. For more general cases, we apply the Feynman–Kac formula and develop an iterative numerical scheme to derive the optimal strategies. We also prove the existence and uniqueness of the solution to the fixed point equation and the convergence of an iterative numerical algorithm. Numerical examples are presented to show the effect of jump intensities on the optimal controls.

Original languageEnglish
Pages (from-to)935-952
Number of pages18
JournalEuropean Journal of Operational Research
Issue number3
Publication statusPublished - 1 Feb 2021
Externally publishedYes


  • Dynamic programming
  • Investment and consumption
  • Life insurance
  • Self-contagious market
  • Stochastic labor income


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