Optimal insurance design under asymmetric Nash bargaining

This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. Under asymmetric Nash bargaining, we show that the Pareto-optimal insurance contract always contains a straight deductible under linear transaction costs and that the deductible disappears if and only if the deadweight cost is zero, regardless of the insurer's bargaining power. We further find that the optimality of no insurance is consistent across all market structures. When the insured's risk preference exhibits decreasing absolute risk aversion, the optimal deductible and the insurer's expected loss decrease in the degree of the insured's risk aversion and thus increase in the insured's initial wealth. In addition, the effect of increasing the insurer's bargaining power on the optimal deductible is equivalent to a pure effect of reducing the initial wealth of the insured. Our results suggest that the well-documented preference for low deductibles could be the result of insurance bargaining.