Optimal Insurance Design Under Narrow Framing

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In this paper, we incorporate a psychological factor called narrow framing into standard vNM expected utility model to explain low insurance purchase rate observed in many insurance markets which are sometimes heavily subsidized by governments. In this psychological model, insurance purchase is not only viewed as a way of transferring wealth from the states of low loss to the states of high loss, but also as a pure gamble against insurance companies. When the received indemnity is lower than the paid insurance premium, the economic agent feels like losing the gamble and vice-versa. We study the insurance demand when coinsurance policy is offered and show that partial insurance is strictly preferred even in case of zero transaction cost. We also discuss the optimal insurance design under narrow framing. It turns out that a (non-linear) coinsurance contract is optimal for losses above a certain threshold. We further allow for possible loss aversion and derive the optimal insurance scheme under both narrow framing and loss aversion. As a result, a flat payment of insurance premium should be applied to some intermediate losses.