On-demand insurance contracts are crucial for the sharing economy. These contracts make use of a simple mechanism in a practical way: People differ in their frequency of exposure as well as the probability of loss; the extra dimension of heterogeneity can be used to screen the insured which leads to welfare improvements (the utility possibility frontier shifts outward). The conditioning on time periods relaxes the incentive compatibility constraint, since high frequency types are risking being uncovered for some time by choosing a different contract. We provide sufficient conditions when a full coverage equilibrium is reached. We also analyze various types of on-demand contracts which are used in practice, both in a Rothschild-Stiglitz and in a Wilson-Miyasaki-Spence framework.