Effects of Competition on Insurance Contract Formation

Michael R. Powers, Joseph Qiu, April Shen and Zhan Shen

North American Actuarial Journal, 2016, vol. 20, issue 3, 298-312

Abstract: For an insurance transaction between a single risk-averse buyer and single risk-neutral seller with positive transaction costs, it is well known that the buyer will prefer a policy contract with an ordinary deductible. More detailed results demonstrate the Pareto optimality of an insurance contract characterized by a deductible (followed by coinsurance) for a single risk-averse buyer and single risk-averse seller. In the present work, we employ a market-game model to solve for the equilibrium insurance contract. This formulation, which approximates the behavior of excess property insurance and property catastrophe reinsurance markets, reveals that the equilibrium policy is described by full insurance up to a given policy limit, with no deductible or coinsurance. Our analysis shows further that this solution persists regardless of the numbers of buyers and sellers in the market, and in particular that the market-game equilibrium does not converge to a Pareto-optimal result because of boundary constraints on the number of sellers. Finally, we test our price-formation mechanism against an important generalization, and find that the policy-limit contract persists.

Date: 2016
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DOI: 10.1080/10920277.2016.1191995

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