/sci/ - Science & Math

Since economics and maths is a science, I thought this would belong here.

Say I start an insurance company. I am the only insurer and there are infinite consumers. The average yearly consumer insures $5000 worth of property, the average yearly claim per consumer is $500 and the rates of inflation and interest vary and are always above 0.1. The problems of moral hazard and adverse selection are assumed not to exist in this model. Assume the consumers and insurer live and transact for an infinite period of time.

Say I insure each consumer the exact value of what is being insured, with the promise of if they have not claimed in a consecutive period of 5 years, they regain their original insurance fee they paid in the 1st year of this consecutive period, e.g. Consumer A pays £5000 per year starting from Year 1 over 5 years and does not claim. Between years 1 and 5 the consumer has paid around £25000 (as prices adjust according to a low level of inflation) to the insurer. At the beginning of Year 6, the insurer pays £5000 (this is not adjusted for inflation, assuming $1 in year one > $1 in year 5) to the consumer and collects slightly more than $5000 from the consumer (as the yearly insurance fee increases according to inflation).

Also assume there are no fixed or running costs. Is it possible for the insurer to earn a supernormal profit in this model if you invest some of the money paid by consumers in a (greater than inflation) interest rate, as well as the profits from each year (i.e. having to pay less to each insurer as a no-claims bonus than what you are paid each year)?