Stochastic Life Insurance Demand: An Application to the Economics of Uncertainty

The main logic behind the demand for life insurance is to hedge against the labor income uncertainty due to premature death of a wage earner. In other words, life insurance is the device by which this labor income uncertainty is handled. For insurers, the uncertainty arises from the lack of knowledge about the age of death of the wage earner. This paper attempts to derive life insurance demand curve theoretically. To derive the optimal path of demand for life insurance, the expected joint utility functions for consumption and legacy subject to the wealth accumulation process in deterministic and stochastic cases are maximized. To find the explicit optimal life insurance demand, the specific utility and bequest functions, which exhibit constant relative risk aversion, are examined. Examining a class of CRRA utility function, the effect of explanatory factors on the life insurance demand is discussed. The paper shows that the effect of loading factor, survival rate, and wealth are negative. The effect of degree of risk aversion and, probability of death are positive on the demand for life insurance.