Actuarial mathematical reserve for the extraction of non-renewable resources from non-negative loss variables

Based on the traditional definition of the actuarial mathematical reserve of a whole life insurance, the mathematical reserve for a non-renewable resource is constructed and studied, which considers the extraction dynamics of this resource as part of the benefit obtained. Although nonrenewable resources are finite, it is assumed that the future lifetime of the resource has an infinite time horizon, and that its distribution is in one of the forms Exponential, Weibull, Gamma, and Chen. A method is also presented that combines a recursive process with the trapezoid rule which, more generally, allows calculating the components of the mathematical reserve, regardless of the complexity of the distribution or the parameters of the future lifetime for the non renewable resource.