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Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations

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  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México, Huixquilucan, Edo. de México 52786, Mexico
    Current address: Av. Universidad Anáhuac, No. 46 Col. Lomas Anáhuac, Huixquilucan, Edo. de México 52786, Mexico.
    These authors contributed equally to this work.)

  • Ekaterina Viktorovna Gromova

    (Department of Applied Mathematics, St. Petersburg State University, Saint Petersburg 198504, Russia
    These authors contributed equally to this work.)

  • Ekaterina Sergeevna Miroshnichenko

    (Bwin Interactive Entertainment AG, 1030 Vienna, Austria)

Abstract

This work presents a two-player extraction game where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. Besides, we delve into the implications of working with logarithmic utility/terminal payoff functions. To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle , and the feedback controllers found by means of the Dynamic Programming technique. Our conclusions include a conjecture on the form of the optimal premia for insuring the extraction tasks; and a comparison for the intensities of the extraction for each player under different phases of the lifetimes of their respective machineries.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1081-:d:379803
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