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

Author

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  • Rigoberto Real-Miranda

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México, Av. Universidad Anáhuac 46, Naucalpan de Juárez 52786, Mexico
    These authors contributed equally to this work.)

  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México, Av. Universidad Anáhuac 46, Naucalpan de Juárez 52786, Mexico
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Rigoberto Real-Miranda & José Daniel López-Barrientos, 2022. "A Geologic-Actuarial Approach for Insuring the Extraction Tasks of Non-Renewable Resources by One and Two Agents," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2242-:d:848439
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    References listed on IDEAS

    as
    1. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    2. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    3. Ekaterina Viktorovna Gromova & José Daniel López-Barrientos, 2016. "A Differential Game Model for The Extraction of Nonrenewable Resources with Random Initial Times — The Cooperative and Competitive Cases," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-19, June.
    4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
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