Asymmetric Nash insurance bargaining between risk-averse parties

In this paper, we investigate asymmetric Nash bargaining in the context of proportional insurance contracts between a risk-averse insured and a risk-averse insurer, both seeking to enhance their expected utilities. We obtain a necessary and sufficient condition for the Pareto optimality of the status quo and derive the optimal Nash bargaining solution when the status quo is Pareto dominated. If the insured’s and the insurer’s risk preference exhibit decreasing absolute risk aversion and the insurer’s initial wealth decreases in the insurable risk in the sense of reversed hazard rate order, we show that both the optimal insurance coverage and the optimal insurance premium increase with the insured’s degree of risk aversion and the insurer’s bargaining power. If the insured’s risk preference further follows constant absolute risk aversion, we find that greater insurance coverage is induced as the insurer’s constant initial wealth increases.