Utility maximization of household with information learning and health shocks

Hao Wang; Tak Kuen Siu; Ning Wang; Rongming Wang

doi:10.1016/j.frl.2025.108241

Utility maximization of household with information learning and health shocks

Hao Wang, Tak Kuen Siu, Ning Wang^*, Rongming Wang

^*Corresponding author for this work

Department of Actuarial Studies and Business Analytics

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Abstract

This paper discusses an optimal investment–consumption–insurance problem for a wage earner incorporating information learning and health shocks. The information learning mechanism is designed based on historical investment performance. Critical illness insurance and life insurance can be purchased to hedge against health risk and mortality risk, respectively. Moreover, the wage earner allocates her wealth among consumption and three financial assets continuously over time to maximize the expected discounted utilities. Using the dynamic programming principle coupled with the Hamilton–Jacobi–Bellman (HJB) equations, we obtain analytical expressions for optimal strategies and the respective value functions under various health states. Finally, numerical examples are provided to illustrate the impacts of health shocks and information learning mechanism on optimal strategies.

Original language	English
Article number	108241
Pages (from-to)	1-13
Number of pages	13
Journal	Finance Research Letters
Volume	86
Issue number	Part A
Early online date	22 Aug 2025
DOIs	https://doi.org/10.1016/j.frl.2025.108241
Publication status	Published - Dec 2025

Bibliographical note

Copyright the Author(s) 2025. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Consumption
HJB equation
Health insurance
Health shocks
Information learning
Investment
Life insurance

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10.1016/j.frl.2025.108241

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title = "Utility maximization of household with information learning and health shocks",

abstract = "This paper discusses an optimal investment–consumption–insurance problem for a wage earner incorporating information learning and health shocks. The information learning mechanism is designed based on historical investment performance. Critical illness insurance and life insurance can be purchased to hedge against health risk and mortality risk, respectively. Moreover, the wage earner allocates her wealth among consumption and three financial assets continuously over time to maximize the expected discounted utilities. Using the dynamic programming principle coupled with the Hamilton–Jacobi–Bellman (HJB) equations, we obtain analytical expressions for optimal strategies and the respective value functions under various health states. Finally, numerical examples are provided to illustrate the impacts of health shocks and information learning mechanism on optimal strategies.",

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AU - Wang, Hao

AU - Siu, Tak Kuen

AU - Wang, Ning

AU - Wang, Rongming

N1 - Copyright the Author(s) 2025. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2025/12

Y1 - 2025/12

N2 - This paper discusses an optimal investment–consumption–insurance problem for a wage earner incorporating information learning and health shocks. The information learning mechanism is designed based on historical investment performance. Critical illness insurance and life insurance can be purchased to hedge against health risk and mortality risk, respectively. Moreover, the wage earner allocates her wealth among consumption and three financial assets continuously over time to maximize the expected discounted utilities. Using the dynamic programming principle coupled with the Hamilton–Jacobi–Bellman (HJB) equations, we obtain analytical expressions for optimal strategies and the respective value functions under various health states. Finally, numerical examples are provided to illustrate the impacts of health shocks and information learning mechanism on optimal strategies.

AB - This paper discusses an optimal investment–consumption–insurance problem for a wage earner incorporating information learning and health shocks. The information learning mechanism is designed based on historical investment performance. Critical illness insurance and life insurance can be purchased to hedge against health risk and mortality risk, respectively. Moreover, the wage earner allocates her wealth among consumption and three financial assets continuously over time to maximize the expected discounted utilities. Using the dynamic programming principle coupled with the Hamilton–Jacobi–Bellman (HJB) equations, we obtain analytical expressions for optimal strategies and the respective value functions under various health states. Finally, numerical examples are provided to illustrate the impacts of health shocks and information learning mechanism on optimal strategies.

KW - Consumption

KW - HJB equation

KW - Health insurance

KW - Health shocks

KW - Information learning

KW - Investment

KW - Life insurance

UR - https://www.scopus.com/pages/publications/105015209060

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DO - 10.1016/j.frl.2025.108241

M3 - Article

SN - 1544-6123

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SP - 1

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JO - Finance Research Letters

JF - Finance Research Letters

IS - Part A

M1 - 108241

ER -

Utility maximization of household with information learning and health shocks

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