Intertemporal Insurance

This paper develops a discrete-time general equilibrium model of insurance using standard techniques of intertemporal finance. The underlying source of uncertainty is modeled as a marked point process. The paper begins by characterizing Walrasian equilibrium on the event tree generated by the accident process. The corresponding Arrow- Debreu-Radner contingent-commodity prices allow the pricing of insurance contracts. A transformation of the underlying probability measure gives an alternative characterization of insurance contract prices plus accumulated payouts as martingales. A direct application of the usual dynamic spanning argument demonstrates that one insurance contract for each type of accident suffices, at least generically, to achieve market completeness. The theory is illustrated by a simple example in which consumers have Cobb-Douglas preferences and experience accidents at a rate which varies across individuals but remains constant over time, the traditional setting for much of insurance theory