Optimal consumption and exploration: A case study in piecewise-deterministic Markov modelling

Annals of Operations Research

Volumn 88, Issue , 1999, Pages 121-137

  Farid, Mohammad ^a   Davis, Mark H A ^b  

^a CITY UNIVERSITY   (United Kingdom)

^b Tokyo Mitsubishi International   (United Kingdom)

Author keywords

Hamilton Jacobi Bellman equation; Markov processes; Non renewable resources; Piecewise deterministic processes; Stochastic optimal control

Indexed keywords

EID: 0042639407     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/a:1018918027153     Document Type: Article

References (15)

1. T.M. Apostol, Mathematical Analysis, Addison-Wesley, 1974.
2. K.J. Arrow, Optimal pricing, use and exploration of uncertain natural resource stocks, Conference on Natural Resource Pricing, Trail Lake, WY, August 1977.
3. G. Barles, Solutions de Viscosité des Equations de Hamilton-Jacobi, Mathematics and Applications 17, Springer, 1994.
4. D.P. Bertsekas, Dynamic Programming and Optimal Control, Vols.1 and 2, Athena Scientific, Belmont, MA, 1995.
5. G. Barles and B. Perthame, Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations, Applied Mathematics and Optimization 21(1990)21-44.
6. D.P. Bertsekas and S.E. Shreve, Stochastic Optimal Control: The Discrete Time Case, Mathematics in Science and Engineering 139, Academic Press, 1978.
7. M.H.A. Davis, Markov Models and Optimizations, Monographs on Statistics and Applied Probability 49, Chapman and Hall, 1993.
8. S.D. Deshmukh and S.R. Pliska, Optimal consumption and exploration of nonrenewable resources under uncertainty, Econometrica 48(1980)177-200.
9. N.A. Derzko and S.P. Sethi, Optimal exploration and consumption of a natural resource: Stochastic case, International Journal of Policy Analysis 5(1981)185-200.
10. N.A. Derzko and S.P. Sethi, Optimal exploration and consumption of a natural resource: Deterministic case, Optimal Control Applications and Methods 2(1981)1-21.
11. M. Farid, Optimal control, piecewise-deterministic processes and viscosity solutions, Ph.D. Thesis, Department of Electrical Engineering, Imperial College, London, 1997.
12. P.S. Hagan, D.E. Woodward, R.E. Caflisch and J.B. Keller, Optimal pricing, use and exploration of uncertain natural resources, Applied Mathematical Finance 1(1994)87-108.
13. M.H.A. Davis and M. Farid, Piecewise-deterministic processes and viscosity solutions, in: Stochastic Analysis, Control, Optimization and Applications. A Volume in Honor of W.H. Fleming, eds. W.M. McEneaney, G. Yin and Q. Zhang, Systems and Control: Foundations and Applications, Birkhäuser, Boston, 1999, pp. 249-268.
14. H.M. Soner, Optimal control of a one-dimensional storage process, Applied Mathematics and Optimization 13(1985)175-191.
15. D. Vermes, Optimal control of piecewise deterministic Markov processes, Stochastics 14(1985) 165-207.