This paper extends existing insurance results on the type of insurance contracts needed for insurance market efficiency to a dynamic setting. It introduces continuosly open markets that allow for more efficient asset allocation. It also eliminates the role of preferences and endowments in the classification of risks, which is done primarily in terms of the actuarial properties of the underlying risk process. The paper further extends insurability to include correlated and catstrophic events. Under these very general conditions the paper defines a condition that determines whether a small number of standard insurance contracts (together with aggregate assets) suffice to complete markets or one needs to introduce such assets as mutual insurance.