Pay-as-you-drive (PAYD) insurance is an exciting innovation. We develop a dynamic model to study PAYD insurance from the policyholder’s utility maximization perspective. We demonstrate that PAYD insurance does benefit the policyholder by reducing premium paid and increasing the total utility derived from auto usage and wealth. PAYD insurance may also improve overall social welfare by incentivizing customers to drive less. We illustrate that PAYD insurance is more efficient than fuel tax in reducing mileage due to the concavity relation of premium and driving distance. Finally, we derive a cut-off value of mileage below which policyholders who drive with traditional insurance should switch to a PAYD policy. Our research proposes a reliable theoretical framework, and confirms that PAYD insurance benefits both individual customers and society as a whole.
Bibliographical noteWe thank Larry Tzeng, Carole Bernard, Qiang Li, Xian Xu, Jiangxing Wu, and participants at the 24th International Congress on Insurance: Mathematics and Economics, 2021 China International Risk Forum, and 2021 China International Conference on Insurance and Risk Management for helpful comments and suggestions.
Jiang Cheng acknowledges the financial support of Lingnan University, HKSAR. Frank Y. Feng is grateful for the support of the Natural Science Foundation of China (72101140, 72073089, 72073090), Postdoctoral Science Foundation of China (No. 2019M651454), and Shanghai Pujiang Program (21PJC051). Xudong Zeng is supported by the National Natural Science Foundation of China (Grant No. 71771142) and by the Fundamental Research Funds for the Central Universities.
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