Optimal portfolio and consumption with habit formation in a jump diffusion market

Xinfeng Ruan*, Wenli Zhu, Jin Hu, Jiexiang Huang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper studies optimal portfolio and consumption selection with habit formation in a jump diffusions incomplete market in continuous-time. The stochastic maximum principle for jump processes is applied to solve habit-forming utility maximization problem. We transform this problem into the case not involving habit formation in mechanically. Then the solution in the state feedback form is given. The relationship between maximum principle and dynamic programming is employed to get the expression of the relative risk aversion (RRA) coefficient and its distribution. Finally, for a special case, the stationary mean of the RRA coefficient is obtained and the numerical experiment indicates our model with jump diffusions is better than the model in [1] to resolve the equity premium puzzle in a way.

Original languageEnglish
Pages (from-to)391-401
Number of pages11
JournalApplied Mathematics and Computation
Publication statusPublished - 2013
Externally publishedYes


  • Equity premium puzzle
  • Habit formation
  • Jump diffusions market
  • Portfolio and consumption
  • Stochastic control
  • The maximum principle


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