Description: Following Jorgensen and Paes De Souza 1994, Tweedie's compound Poisson distribution is fitted to private passenger automobile accident benefit data. The Tweedie process is a three parameter distribution which corresponds to a Poisson process for claim frequency with gamma distributed claim sizes. From Actuarial Research Conference 1995.

Description: Typically, policyholders do not purchase property/casualty insurance only once in their lifetimes, but make annual decisions concerning insurance purchases. In most personal and commercial lines of insurance, contracts are renewed annually and relationships between insurers and policyholders often include significant past history. To reflect this reality, it would be beneficial to have a theoretical multiple period model of the property/casualty insurance industry. Rothschild and Stiglitz's [1976] one period model of the insurance industry predicts that equilibrium in the marketplace exists in which consumers with differing risk propensities purchase varying amounts of insurance. A multiple period extension of Rothschild and Stiglitz's model can be constructed in which a consumer's future contract choice is contingent on her past contract choice. As in the one period Rothschild-Stiglitz model, a consumer reveals her risk type through the amount of coverage purchased in the period of separation. Since the contract purchased reveals the consumer type, future policies must be conditioned on this information and as such future contracts are contingent on past contracts. Unfortunately, in personal lines of property-casualty insurance, policies are not typically contingent on past policy choices. Future contract provisions, either the amount of insurance offered, or the price of insurance, are usually contingent on the past accident histories of the insureds and not on the amounts of insurance purchased. Two possible reasons given in the literature for this are that contracting insurers cannot restrict the amount of insurance bought from other insurance companies and so the amount cannot be used as a screening mechanism, and that insureds are unaware of their risk type. This paper provides another conjecture as to why these contracts, denoted Rothschild-Stiglitz contracts, are not observed in the market place. Quite simply, the cost of revealing one's type

Description: The purpose of this paper is to explore the capital holdings of Canadian property/casualty insurers, taking regulatory requirements as given. In particular, it addresses the following issues: 1. Are firms in fact over capitalized with respect to mandated capital adequacy thresholds? 2. Do higher capital holdings translate into lower returns on equity [ROEs] for firms? 3. Is there a relationship between Best’s Ratings and a firm’s capital holdings, as shown to be in the United States? 4. Which firm characteristics are important in determining capital holdings?