Jaśkiewicz, Anna and Matkowski, Janusz and Nowak, Andrzej S. (2011): On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models. Forthcoming in: Annals of Operations Research : pp. 115.

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Abstract
This paper generalizes the classical discounted utility model introduced by Samuelson by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski's extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal growth with unbounded utility functions.
Item Type:  MPRA Paper 

Original Title:  On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models 
English Title:  On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models 
Language:  English 
Keywords:  Dynamic programming Variable discounting Bellman equation 
Subjects:  D  Microeconomics > D9  Intertemporal Choice and Growth > D90  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  31069 
Depositing User:  Andrzej Nowak 
Date Deposited:  24. May 2011 10:36 
Last Modified:  14. Feb 2013 10:45 
References:  Alvarez F, Stokey N (1998) Dynamic programming with homogeneous functions. J Econ Theory 82: 167189 Becker RA, Boyd III JH (1997) Capital theory, equilibrium analysis and recursive utility. Blackwell Publishers, New York Benzion U, Rapoport A, Yagil J (1989) Discount rates inferred from decisions: an experimental study. Manage Sci 35: 270284 Berge C (1963) Topological spaces. MacMillan, New York Bhattacharya R, Majumdar M (2007) Random dynamical systems: theory and applications. Cambridge University Press, Cambridge, MA Blackwell D (1965) Discounted dynamic programming. Ann Math Statist 36: 226235 Boyd III JH (1990) Recursive utility and the Ramsey problem. J Econ Theory 50: 326345 Boyd III JH (2006) Disretetime recursive utility. In: Dana RA, Le Van C, Mitra T, Nishimura K (eds) Handbook of optimal growth 1, discrete time. SpringerVerlag, New York pp. 251272 Denardo EV (1967) Contraction mappings in the theory underlying dynamic programming. SIAM Rev 9: 165177 Dugundji J, Granas A (2003) Fixed point theory. SpringerVerlag, New York Epstein L, Hynes JA (1983) The rate of time preference and dynamic economic analysis. J Polit Econ 91: 611635 Feinberg EA (2002) Total reward criteria. In: Feinberg EA, Shwartz A (eds) Handbook of Markov decision processes. Kluwer Publishers, Boston pp. 173207 Frederick S, Loewenstein G, O'Donoghue T (2002) Time discounting and time preference: a critical review. J Econ Lit 11: 351401 Green L, Myerson J, McFadden E (1997) Rate of temporal discounting decreases with amount of reward. Memory and Cognition 25: 715723 HernandezLerma O, Lasserre JB (1996) Discretetime Markov control processes: basic optimality criteria. SpringerVerlag, New York HernandezLerma O, Lasserre JB (1999) Further topics on discretetime Markov control processes. SpringerVerlag, New York Hinderer K (1970) Foundations of nonstationary dynamic programming with discrete time parameter. Lecture Notes in Oper Res 33, SpringerVerlag, New York Kirby KN (1997) Bidding on the future: evidence against normative discounting of delayed rewards, J Exper Psych: General 126: 5470 Koopmans TC (1960) Stationary ordinal utility and impatience. Econometrica 28: 287309 Kreps DM, Porteus EL (1978) Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46: 185200 Le Van C, Morhaim L (2002) Optimal growth models with bounded or unbounded returns: a unifying approach. J Econ Theory 105: 158187 Le Van C, Vailakis Y (2005) Recursive utility and optimal growth with bounded or unbounded returns. J Econ Theory 123: 187209 Lucas RE, Stokey N (1984) Optimal growth with many consumers. J Econ Theory 32: 139171 Marinacci M, Montrucchio L (2010) Unique solutions for stochastic recursive utilities. J Econom Theory 145: 17761804 Matkowski J (1975) Integral solutions of functional equations. Dissertationes Mathematicae 127: 168 Ramsey FP (1928) A mathematical theory of saving. Econ J 38: 543599 RinconZapatero JP, RodriguezPalmero C (2003) Existence and uniqueness of solutions to the Bellman equation in the unbounded case. Econometrica 71: 15191555 RinconZapatero JP, RodriguezPalmero C (2009) Corrigendum to ``Existence and uniqueness of solutions to the Bellman equation in the unbounded case''. Econometrica 71 (2003), 15191555. Econometrica 77: 317318 Samuelson P (1937) A note on measurement of utility. Rev of Econ Stud 4: 155161 Schal M (1975) Conditions for optimality in dynamic programming and for the limit of nstage optimal policies to be optimal. Z Wahrsch verw Geb 32: 179196 Stokey NL, Lucas RE, Prescott E (1989) Recursive methods in economic dynamics. Harvard University Press, Cambridge, MA Strauch R (1966) Negative dynamic programming. Ann Math Statist 37: 871890 Thaler RH (1981) Some empirical evidence on dynamic inconsistency. Econ Lett 8: 201207 Uzawa H (1968) Time preference, the consumption function, and optimum asset holding. In: Wolfe JN (ed) Value, capital and growth: papers in honor of Sir John Hicks. Edinburgh University Press, Edinburgh pp. 485504 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/31069 