No Claim? Your Gain: Design of Residual Value Extended Warranties Under Risk Aversion and Strategic Claim Behavior

Abstract

Traditional one-price-for-all extended warranties do not differentiate customers according to their risk attitudes, usage rates, or operating environment. These warranties are priced to cover the cost of high-usage customers who have more failures and are willing to pay a risk premium for their risk aversion. That makes traditional warranties economically unattractive to low-usage customers and those who are less risk averse. These issues can be addressed by residual value warranties, which refund part of the up-front price to customers who have zero or few claims according to a predetermined refund schedule. Residual value warranties may induce strategic claim behavior, since customers may prefer to pay for small failures out of pocket rather than claim failures now and give up potential refunds later. We design and price residual value warranties to maximize expected profits, taking into account strategic claim behavior and risk attitudes. For the constant absolute risk aversion model, we characterize customers’ optimal claim strategy as well as the net value and support cost for residual value warranties. Surprisingly, the total support cost to the service provider, including repair costs and refunds, is lower for more risk-averse customers under the residual value warranties, whereas their willingness to pay is higher. As contingent contracts, residual value warranties can better price discriminate customers than traditional warranties. We identify conditions under which residual value warranties are strictly more profitable than traditional warranties in a homogeneous market, as well as in heterogeneous markets that differ in various dimensions, such as risk attitude, failure rate, and repair cost.