“…Among the wide spectrum of feasible insurance indemnity schedules, those with the non-decreasing and 1-Lipschitz condition (i.e., those I such that 0 ≤ I(x) − I(y) ≤ x − y for all y ≤ x), also informally known as the slowly growing condition, have unquestionably gained in popularity in the recent insurance literature. Ensuring that the indemnified loss never increases faster than the policyholder's ground-up loss, the non-decreasing and 1-Lipschitz condition has been used in an abundance of papers as a starting point for formulating optimal (re)insurance policies, which are typically in the form of insurance layers, see, for example, Chi and Tan (2011), Cai et al (2017), Cheung and Lo (2017), and Lo (2017). For all the mathematical benefits it brings, theoretical or empirical justifications of the economic suitability and practical relevance of the non-decreasing and 1-Lipschitz condition to the insurance business have long been lacking, undermining the conceptual foundation of many existing results it underlies.…”