Supplement to Capital Mobility and Asset Pricing Additional Appendices

We illustrate the model with an example motivated by catastrophe insurance contracts. In a particular market, at each of the event times of a Poisson process J with a constant intensity η, a catastrophe occurs that causes losses throughout a population of consumers who are potential buyers of protection. Each of a continuum of consumers in the given insurance market has a property that experiences a loss at each catastrophe event. The losses of the consumers at a given event are identically and symmetrically distributed. The distribution of consumer losses at each catastrophe has the property that if a quantity x of the consumers have bought insurance at the time of the i-th catastrophe, then total claims of xζi are paid by sellers of protection, where ζ1, ζ2, . . . is a sequence of independent random variables, identically distributed on [0, 1], and independent of J . For this, it need not be the case that the damage of a particular consumer at the i-th event is equal to the average damage rate ζi, but we will assume so for notational simplicity only. Each consumer chooses to be insured, or not, at each point in time, based on information available up to that time, but of course not including the information about loss events at precisely that time. Whenever insured, the consumer pays premiums at the current rate pt in his or her market, and is covered against damages in the event of a loss. The appropriate measurability restriction is “predictability.”