Journal of Dynamics and Games (JDG)

On the Euler equation approach to discrete--time nonstationary optimal control problems
Pages: 57 - 78, Issue 1, January 2014

doi:10.3934/jdg.2014.1.57      Abstract        References        Full text (473.6K)           Related Articles

David González-Sánchez - Departamento de Matemáticas, Instituto Tecnológico Autónomo de México (ITAM), Río Hondo 1, México D.F. 01000, Mexico (email)
Onésimo Hernández-Lerma - Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, Mexico (email)

1 D. Acemoglu, "Introduction to Modern Economic Growth," Princeton University Press, Princeton, 2009.
2 J. Adda and R. Cooper, "Dynamic Economics. Quantitative Methods and Applications," MIT Press, Cambridge, MA, 2003.
3 V. I. Arkin and I. V. Evstigneev, "Stochastic Models of Control and Economic Dynamics," Academic Press, Orlando, FL, 1987.
4 Y. Bar-Ness, The discrete Euler equation on the normed linear space $l_n^1$, Int. J. Control, 21 (1975), 625-640.       
5 W. A. Brock and L. Mirman, Optimal economic growth and uncertainty: The discounted case, J. Econ. Theory, 4 (1972), 479-513.       
6 J. A. Cadzow, Discrete calculus of variations, Int. J. Control, 11 (1970), 393-407.
7 G. C. Chow, "Dynamic Economics: Optimization by the Lagrange Method," Oxford University Press, New York, 1997.
8 I. Ekeland and J. A. Scheinkman, Transversality conditions for some infinite horizon discrete time optimization problems, Math. Oper. Res., 11 (1986), 216-229.       
9 S. Elaydi, "An Introduction to Difference Equations," Third edition, Undergraduate Texts in Mathematics, Springer, New York, 2005.       
10 J. Engwerda, "LQ Dynamic Optimization and Differential Games," John Wiley & Sons, Chichester, 2005.
11 S. Flåm and A. Fougères, Infinite horizon programs; Convergence of approximate solutions, Ann. Oper. Res., 29 (1991), 333-350.       
12 W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control," Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975.       
13 X. Guo, A. Hernández-del-Valle and O. Hernández-Lerma, Nonstationary discrete-time deterministic and stochastic control systems: Bounded and unbounded cases, Systems Control Lett., 60 (2011), 503-509.       
14 O. Hernández-Lerma and J. B. Lasserre, "Discrete-Time Markov Control Processes: Basic Optimality Criteria," Applications of Mathematics (New York), 30, Springer-Verlag, New York, 1996.       
15 T. Kamihigashi, A simple proof of the necessity of the transversality condition, Econ. Theory, 20 (2002), 427-433.       
16 T. Kamihigashi, Transversality conditions and dynamic economic behaviour, in "The New Palgrave Dictionary of Economics" (eds. S. N. Durlauf and L. E. Blume), Second edition, Palgrave Macmillan, Hampshire, (2008), 384-387.
17 W. G. Kelley and A. C. Peterson, "Difference Equations. An Introduction with Applications," Academic Press, Inc., Boston, MA, 1991.       
18 C. Le Van and R.-A. Dana, "Dynamic Programming in Economics," Dynamic Modeling and Econometrics in Economics and Finance, 5, Kluwer Academic Publishers, Dordrecht, 2003.       
19 D. Levhari and L. D. Mirman, The great fish war: An example using dynamic Cournot-Nash solution, Bell J. Econom., 11 (1980), 322-334.       
20 L. Ljungqvist and T. J. Sargent, "Recursive Macroeconomic Theory," Second edition, MIT Press, Cambridge, MA, 2004.
21 D. G. Luenberger, "Optimization by Vector Space Methods," John Wiley & Sons, Inc., New York-London-Sydney, 1969.       
22 K. Okuguchi, A dynamic Cournot-Nash equilibrium in fishery: The effects of entry, Riv. Mat. Sci. Econom. Social., 4 (1981), 59-64.       
23 W. Rudin, "Principles of Mathematical Analysis," Third edition, McGraw-Hill Book Co., New York-Auckland-Düsseldorf, 1976.       
24 I. Schochetman and R. L. Smith, Finite dimensional approximation in infinite-dimensional mathematical programming, Math. Programming, 54 (1992), 307-333.       
25 N. L. Stokey, R. E. Lucas and E. C. Prescott, Jr., "Recursive Methods in Economic Dynamics," With the collaboration of Edward C. Prescott, Harvard University Press, Cambridge, MA, 1989.       
26 K. Sydsæter, P. J. Hammond, A. Seierstad and A. Strøm, "Further Mathematics for Economic Analysis," Second edition, Prentice-Hall, New York, 2008.

Go to top