A Long-Term Mathematical Model for Mining Industries

Article English OPEN
Achdou, Yves; Giraud, Pierre-Noël; Lasry, Jean-Michel; Lions, Pierre-Louis;
(2016)
  • Publisher: Springer Verlag (Germany)
  • Identifiers: doi: 10.1007/s00245-016-9390-0
  • Subject: Viscosity solution | Master equation | Heterogeneous agents model | [INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] | [SHS.ECO]Humanities and Social Sciences/Economics and Finance | Model calibration | Mean field games | Hamilton Jacobi equations

International audience; A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection ... View more
  • References (5)

    [9] J.-M. Lasry and P.-L. Lions, Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I. The model problem, Math. Ann. 283 (1989), no. 4, 583{ 630. MR 990591

    [10] J-M. Lasry and P-L. Lions, Jeux a champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris 343 (2006), no. 9, 619{625. MR MR2269875 (2007m:91021) [11] [12] , Jeux a champ moyen. II. Horizon ni et contr^ole optimal, C. R. Math. Acad. Sci. Paris 343 (2006), no. 10, 679{684. MR MR2271747 (2007m:91022) , Mean eld games, Jpn. J. Math. 2 (2007), no. 1, 229{260. MR MR2295621

    [13] P.L Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics 69, Pitman, Boston, 1982.

    [14] R. E. Lucas, Jr. and E. C. Prescott, Investment under uncertainty, Econometrica 39 (1971), 659{681. MR 0398471

    [15] H. M. Soner, Optimal control with state-space constraint. I, SIAM J. Control Optim. 24 (1986), no. 3, 552{561. MR MR838056 (87e:49029) , Optimal control with state-space constraint. II, SIAM J. Control Optim. 24 (1986), no. 6, 1110{1122. MR MR861089 (87k:49021)

  • Metrics
Share - Bookmark