A LIFE CYCLE MODEL OF LIFE INSURANCE PURCHASES*

A LIFE CYCLE MODEL OF LIFE INSURANCE PURCHASES*

BY STANLEY FISCHER1

1. INTRODUCTION

Lifetime consumption models and portfolio decisions have been presented by Hokinson (2), Mossin (10), Samuelsson (11), Merton (9), David Lewahri and Srinivasan [6] and others. They either deal with an infinite horizon or with the date of death being known with certainty. Yaris (12) has studied the problem of uncertain life and life insurance in the context of the expected utility assumption using a continuous-time model. He describes the optimal paths of consumption and saving by means of two differential equations that must be satisfied along these paths, but he does not examine in detail the demand functions for consumption or insurance. Hokinson (3) has also considered the problem of consumption and portfolio choice under lifetime uncertainty, using a discrete-time model.

In this paper we use a discrete-time model, essentially similar to Hokinson (3) in which the length of life is uncertain, to examine the life-cycle patterns of consumption, saving, and insurance purchases.

The emphasis in the present paper is on comparative statistics and dynamics of insurance demand functions rather than on the existence of a solution to the problem. For most of the paper, it is assumed that there are only two assets—a bond, and an insurance asset—so that the uncertainty is limited to the uncertainty on the date of death. Several simulations of the model are presented in the study of its dynamics. The model used and the specific assumptions are described in Section 2. In Section 3 the only assets are single-period insurance and single-period bonds. As in most of the literature on portfolio selection over the life span, the individual is assumed to have an initial wealth accumulation and to earn no income. The introduction of the full-income wealth model is deferred until Section 5, especially for external purposes. In Section 4, an additional risky asset, equity, is introduced. In Section 5, labor income is added.

It is shown that the expected receipt of such income increases the demand for life insurance. In Section 6, consumers are allowed to purchase both single-term and two-term term insurance.