A Characterization of Life Expectancy with Applications to Loss Models

In its usual (one-dimensional) form, a loss model is just a distribution of nonnegative real numbers [O, Qo). This note establishes necessary and sufficient conditions for a differentiable function to equal the life expectancy of some loss model. Examples are provided to illustrate the shape of the life expectancy function of several common loss models. The characterization is used to define a general class of loss models flexible enough to cover the Pareto, Lognormal, Weibull, and Gamma densities. Finally, the approach is extended to model multi-dimensional survivorship.