A Geologic-Actuarial Approach for Insuring the Extraction Tasks of Non-Renewable Resources by One and Two Agents

Rigoberto Real-Miranda and José Daniel López-Barrientos
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Rigoberto Real-Miranda: Facultad de Ciencias Actuariales, Universidad Anáhuac México, Av. Universidad Anáhuac 46, Naucalpan de Juárez 52786, Mexico
José Daniel López-Barrientos: Facultad de Ciencias Actuariales, Universidad Anáhuac México, Av. Universidad Anáhuac 46, Naucalpan de Juárez 52786, Mexico

Mathematics, 2022, vol. 10, issue 13, 1-19

Abstract: This work uses classic stochastic dynamic programming techniques to determine the equivalence premium that each of two extraction agents of a non-renewable natural resource must pay to an insurer to cover the risk that the extraction pore explodes. We use statistical and geological methods to calibrate the time-until-failure distribution of extraction status for each agent and couple a simple approximation scheme with the actuarial standard of Bühlmann’s recommendations to charge the extracting agents a variance premium, while the insurer earns a return on its investment at risk. We test our analytical results through Monte Carlo simulations to verify that the probability of ruin does not exceed a certain predetermined level.

Keywords: extraction game for two agents; time-until-failure; hazard rates; vertical pressure gradient; Bühlmann recommendations for premium calculation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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