The Discrete-Time Models for an Individual's Life Insurance, Consumption and Stock Purchase Decisions¹

Abstract

Yanyun (Judy) Zhu
Assistant Professor At the University of Illinois at Urbana-Champaign

Depending on his risk attitude and the form of his utility function, an individual's life insurance and stock purchases are either independent of each other or positively related with each other: With a constant risk attitude (at all levels of wealth) and an exponential utility function, the two decisions are independent of each other. But with a decreasing risk attitude (when the individual becomes wealthier) and a power utility function, the two decisions are positively related with each other and consequently, any factor that affects the stock purchase will also affect the life insurance purchase, and vice versa.

When deciding how much to spend on consumption, life insurance, and stock purchases, an individual will consider: (1) His current level of wealth and future income, his health status and survival probability, his attitudes toward risk and bequest, and his preference of current to future consumption. (2) The insurance market conditions, such as the insurance premium and surrender value. (3) The financial market conditions, such as the risk free rate of return, the stock return and volatility.

¹ This is part of my dissertation, which was finished at the University of Wisconsin-Madison in 2003 under the supervision of Professor Virginia R. Young (Chair), Mark J. Browne, Edward W. Frees, Thomas G. Kurtz, and Marjorie A. Rosenberg.

Contact: jzhu@uiuc.edu ; 217.244.6156.

From studying his life insurance purchase behavior (along with his choices on consumption and stock purchase), I find an individual buys life insurance mainly to protect his dependents against suffering the financial distress at his sudden death. Particularly, I find an individual will buy more life insurance when his future income is larger and thus the financial loss is more severe at his death; when he cares more about his dependents' welfare; or when he is more averse to risk and uncertainty. Also I find that life insurance is a normal good and any factor that contributes to the reduction of insurance premiums, such as an increased survival probability or reduced expense loadings, will encourage the individual to purchase more of life insurance.

After purchasing an insurance policy, an individual has the option to keep it or terminate it. The individual will start to surrender his policy when his future income decreases, his bequest motive disappears, or his insurance premium increases.

My above studies involve both one-period and two-period models and the results from the two are consistent with each other.