On non-monotonic ageing properties from the Laplace transform, with actuarial applications

Non-monotonic ageing has been considered in the literature to model situations where initially the residual lifetime tends to decrease (increase) and after a certain period, it starts to increase (decrease) with increasing age. On the other hand, the Laplace transform has been used to represent actuarial amounts, such as indemnities associated with risks, incomes associated with financial transactions or life premiums in life insurance. In this paper we introduce a new concept to describe non-monotonic ageing in actuarial sciences which is defined in terms of the Laplace transform of the residual life, and we derive its relationship with the net prospective premium reserve. We obtain some properties and applications in insurance related to this ageing class, the relationships among some non-monotonic ageing classes in the literature and closure under shock models, as well as several comparisons among the change points. Some illustrative examples are provided.