Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity

Tao Wang and Zhiping Chen

Insurance: Mathematics and Economics, 2024, vol. 118, issue C, 195-222

Abstract: This paper studies the optimal consumption, investment, health insurance and life insurance strategy for a wage earner with smooth ambiguity, habit formation and biometric risks. The individual can invest in the financial market composed of a risk-free asset and a risky asset whose unknown market price results in ambiguity. The habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the biometric risks, which consist of health shock risk and mortality risk, can impact the individual's income and health state. The individual can purchase health insurance and life insurance to respectively deal with health shock risk and mortality risk, and aims at maximizing the total expected utility of consumption, legacy and terminal wealth. Using the dynamic programming technique, we derive the corresponding Hamilton-Jacobi-Bellman equation in the states of health and critical illness respectively, prove the verification theorem and obtain closed-form solutions for the optimal strategies. Finally, numerical experiments are carried out to illustrate the impact of risk aversion, ambiguity aversion, health shock and habit formation on the optimal strategy. The results reveal that the wage earner with different utility functions and different health states will show different behaviors in consumption, investment and insurance purchase.

Keywords: Biometric risks; Smooth ambiguity; Habit formation; Health insurance; Hamilton-Jacobi-Bellman equation (search for similar items in EconPapers)
JEL-codes: C61 G11 I13 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668724000805
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:118:y:2024:i:c:p:195-222

DOI: 10.1016/j.insmatheco.2024.07.002

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().