Resource exploitation in a stochastic horizon under two parametric interpretations

José Daniel López-Barrientos, Ekaterina Viktorovna Gromova, Ekaterina Sergeevna Miroshnichenko

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7 Scopus citations

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.

Original languageEnglish
Article number1081
JournalMathematics
Volume8
Issue number7
DOIs
StatePublished - 1 Jul 2020

Keywords

  • Chen distribution
  • Differential games
  • Discounted equilibrium
  • Equivalence principle
  • Random time horizon
  • Time until failure
  • Weibull distribution

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