A Life Cycle Model of Life Insurance Purchases
by Hakansson [2], Mossin [10], Samuelson [11], Merton [9], Levhari and Srinivasan [6], and others. These either deal with an infinite horizon or take the date of death to be known with certainty. Yaari [12] has studied the problem of uncertain lifetime and life insurance in the context of the expected utility hypothesis using a continuous time model; he characterizes the optimal paths of consumption and savings by two differential equations which must be satisfied on these paths, but does not examine demand functions for consumption or insurance in detail. Hakansson [3], using a discrete-time model, has also considered the problem of consumption and portfolio choices when the lifetime is uncertain. In this paper we use a discrete-time model, which is essentially similar to that of Hakansson [3], in which the length of life is uncertain, to examine life-cycle patterns of consumption, savings and insurance purchases. The emphasis in the present paper is on the comparative statics and dynamics of the 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 uncertainty is confined to uncertainty over the date of death. A number of simulations of the model are presented in studying its dynamics.