Aoki, Takaaki (2013): Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Twosided Altruism Dynamics.

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Abstract
This article describes some dynamic aspects on dynastic utility incorporating twosided altruism with an OLG setting. We analyzed the special case where the weights of twosided altruism are dynamically inconsistent. The Bellman equation for twosided altruism proves to be reduced to onesided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of selfconsistent policy functions with distinct steady states (indeterminacy of selfconsistent policy functions).
Item Type:  MPRA Paper 

Original Title:  Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Twosided Altruism Dynamics 
English Title:  Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Twosided Altruism Dynamics 
Language:  English 
Keywords:  Bellman equation, Twosided altruism, Dynamic inconsistency, Selfconsistent policy functions, Indeterminacy, Overlapping generations model. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis D  Microeconomics > D9  Intertemporal Choice > D91  Intertemporal Household Choice ; Life Cycle Models and Saving O  Economic Development, Innovation, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity > O41  One, Two, and Multisector Growth Models 
Item ID:  44994 
Depositing User:  Takaaki Aoki 
Date Deposited:  01. Aug 2013 15:21 
Last Modified:  01. Aug 2013 17:07 
References:  Abel A. B. (1987) "Operative Gift and Bequest Motives", American Economic Review, 77/5, 10371047. Aoki T. (2011) "On the Implications of TwoSided Altruism in Human Capital Based OLG Model", Asian Journal of Law and Economics, 2/2. Araujo A. (1991) "The once but not twice differentiability of the policy function", Econometrica, 59/ 5, 13831393. Bellman R. (1957) Dynamic Programming, Princeton, Princeton University Press. Benveniste, LM. and Scheinkman J. A. (1979) "On the Differentiability of the Value Function in Dynamic Models of Economics", Econometrica, 47/3, 727732. Blackwell D. (1965) "Discounted Dynamic Programming", Annals of Mathematical Statistics, 36, 226235. Boldrin M. and Montrucchio L. (1986) "On the Indeterminacy of Capital Accumulation Paths", Journal of Economic Theory, 40/1, 2639. Geanakoplos J. and Brown D. J. (1985) "Comaparative Statics and Local Indeterminacy in OLG Economics: An Application of the Maultiplicative Ergodic Theorem", Cowles Foundation Discussion Paper, 773. Hori H. (1997) "Dynamic Allocation in an Altruistic Overlapping Generations Economy", Journal of Economic Theory, 73/2, 292315. Hori H. and Kanaya S. (1989) "Utility Functionals with Nonpaternalistic Intergenerational Altruism", Journal of Economic Theory, 49, 241265. Kimball M. S. (1987) "Making Sense of TwoSided Altruism", Journal of Monetary Economics, 20/2, 301326. Mitra T. (2000) "Introduction to Dynamic Optimization Theory", Optimization and Chaos, Majumdar, Mukal, Tapan Mitra and Kazuo Nishumura eds, Studies in Economic Theory, Springer. Montrucchio L. (1987) "Lipschiz continuous policy functions for strongly concave optimization problems", Journal of Mathematical Economics, 16, 259273. Pontryagin, L. S. and Associates (1962) The Mathematical Theory of Optimal Processes, New York: Interscience. Santos M. S. (1991) "Smoothness of the Policy Function in Discrete Time Economic Models", Econometrica, 59/5, 13651382. Stokey N. and Lucas R. E. (1989) Recursive Methods in Economic Dynamics, Harvard University Press. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/44994 