Discontinuous solutions of deterministic optimal stopping time problems

G. Barles; B. Perthame

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 4, page 557-579
  • ISSN: 0764-583X

How to cite

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Barles, G., and Perthame, B.. "Discontinuous solutions of deterministic optimal stopping time problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.4 (1987): 557-579. <http://eudml.org/doc/193514>.

@article{Barles1987,
author = {Barles, G., Perthame, B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {discontinuous obstacle; deterministic optimal stopping time problem; viscosity solution; Bellman variational inequality; minimum exit time from a domain},
language = {eng},
number = {4},
pages = {557-579},
publisher = {Dunod},
title = {Discontinuous solutions of deterministic optimal stopping time problems},
url = {http://eudml.org/doc/193514},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Barles, G.
AU - Perthame, B.
TI - Discontinuous solutions of deterministic optimal stopping time problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 4
SP - 557
EP - 579
LA - eng
KW - discontinuous obstacle; deterministic optimal stopping time problem; viscosity solution; Bellman variational inequality; minimum exit time from a domain
UR - http://eudml.org/doc/193514
ER -

References

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  1. [1] I. CAPUZZO-DOLCETTA and H. ISHII, Approximate solutions of the Bellman Equations of deterministic control theory. Applied Math, andOpt. 11, (1984),pp. 161-181. Zbl0553.49024MR743925
  2. [2] I. CAPUZZO-DOLCETTA and P. L. LIONS, Hamilton-JacobiEquations and state- constraints problems ; In preparation. Zbl0702.49019
  3. [3] M. G. CRANDALL, L. C. EVANS and P. L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi Equations ; Trans. Amer. Math. Soc., 282 (1984). Zbl0543.35011MR732102
  4. [4] M. G. CRANDALL, H. ISHII, and P. L. LIONS, Uniqueness of viscosity solutions revisited ; to appear. Zbl0644.35016
  5. [5] M. G. CRANDALL and P. L. LIONS, Viscosity solutions of Hamilton-Jacobi Equations ; Trans. Amer. Math. Soc., 277 (1983). Zbl0599.35024MR690039
  6. [6] M. G. CRANDALL and P. L. LIONS, On existence and uniqueness of solutions of Hamilton-Jacobi Equations ; Non Linear Anal. TMA. Vol. 10, N°6 (1986). Zbl0603.35016MR836671
  7. [7] W. H. FLEMING and R. W. RISHEL, Deterministic and stochastic optimal control. Springer, Berlin 1975. Zbl0323.49001MR454768
  8. [8] H. ISHII, Hamilton-Jacobi Equations with discontinuous Hamiltonians on arbitrary open subsets. Zbl0937.35505
  9. [9] H. ISHII, Perron's method for Hamilton-Jacobi Equations ; to appear. Zbl0697.35030
  10. [10] E. B. LEE and L. MARKUS, Foundations of optimal control theory, J. Wiley, New York (1967). Zbl0159.13201MR220537
  11. [11] P. L. LIONS, Generalized solutions of Hamilton-Jacobi Equations. Pitman, 1982. Zbl0497.35001MR667669
  12. [12] P. L. LIONS and B. PERTHAME, Remarks on Hamilton-Jacobi Equations with discontinuous time-dependent coefficients ; Non Linear Anal. TMA. Vol. 11, n° 7 (1987). Zbl0688.35052MR886652
  13. [13] P. L. LIONS and P. E. SOUGANIDIS, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaac's Equations ; SIAM J. Control and Optimization, vol. 23, n° 4 (1985). Zbl0569.49019MR791888
  14. [14] J. P. QUADRAT, in Thèse d'Etat, Univ. Paris IX-Dauphine. Zbl0546.22019
  15. [15] M. H. SONER, Optimal controlproblems with state-space constraints. SIAM J.on Control and Optimisation. Vol. 24, n° 3, pp. 551-561 and Vol. 24, n° 4, pp. 1110-1122. Zbl0619.49013MR861089
  16. [16] J. WARGA, Optimal control of differential and functionnal equations. Academic press, (1972). Zbl0253.49001MR372708

Citations in EuDML Documents

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  1. Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani, Deterministic state-constrained optimal control problems without controllability assumptions
  2. Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani, Deterministic state-constrained optimal control problems without controllability assumptions
  3. I. Capuzzo Dolcetta, M. Falcone, Discrete dynamic programming and viscosity solutions of the Bellman equation
  4. Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
  5. Magdalena Kobylanski, Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
  6. G. Barles, An approach of deterministic control problems with unbounded data
  7. Bertram Düring, Michel Fournié, Ansgar Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
  8. Pierpaolo Soravia, Degenerate Eikonal equations with discontinuous refraction index
  9. Italo Capuzzo Dolcetta, Soluzioni di viscosità

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