Actuarial modeling of battery insurance for electric vehicles

This paper develops a stochastic framework for modeling battery capacity degradation, with the aim of designing insurance products for electric vehicles. The degradation process is first described by a Brownian motion with drift, leading to a tractable distribution of the lifetime defined as the first passage time below a failure threshold. Heterogeneity across vehicles is then incorporated through random effects reflecting battery type and individual behavior, thereby inducing correlations between failure times analogous to systematic components in mortality models. The proposed approach emphasizes distributional modeling of lifetimes rather than real-time prediction, thus aligning battery insurance with traditional life insurance mathematics while distinguishing it from much of the engineering literature devoted to remaining useful life. The proposed approach is illustrated with a simple numerical example performed on simulated data.