The Valuation of Multiple Claim Insurance Contracts

A closed form solution is provided for the value of a multiple claim insurance contract that is subject to a deductible amount and an upper limit on claims. The solution is a time integral of European option prices. A model is developed that abstracts from problems of market imperfections, noncompetitiveness, nonobservability, adverse selection, and moral hazard. The model examines the pricing of insurance policies in an environment where claims are generated according to exogenously specified stochastic processes. The model provides 3 important insights: 1. Systematic risk in insurance policies is altered in the presence of deductibles and maximum indemnity levels. 2. Idiosyncratic risk affects policy valuation and the required rates of return on underwriting portfolios. 3. Contrary to traditional actuarial intuition, changes in the risk-free interest rate may either increase or reduce policy values.