Reserva matemática actuarial para la extracción de recursos no-renovables a partir de variables de pérdida no-negativas

Rigoberto Real-Miranda; José Daniel López-Barrientos

doi:10.24310/recta.23.2.2022.19875

Authors

Rigoberto Real-Miranda Universidad An´ahuac
José Daniel López-Barrientos Universidad An´ahuac

DOI:

https://doi.org/10.24310/recta.23.2.2022.19875

Keywords:

Reserva matem´atica actuarial, programaci´on din´amica, recurso no-renovable, proceso recursivo, regla del trapecio, juegos diferenciales

Abstract

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.

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