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Optimal control with heterogeneous agents in continuous time

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  • Nuño, Galo
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    Abstract

    This paper introduces the problem of a planner who wants to control a population of heterogeneous agents subject to idiosyncratic shocks. The agents differ in their initial states and in the realization of the shocks. In continuous time, the distribution of states across agents is described by a Kolmogorov forward equation. The planner chooses the controls in order to maximize an optimality criterion subject to an .aggregate resource constraint. We demonstrate how the solution should satisfy a system of partial differential equations that includes a generalization of the Hamilton-Jacobi-Bellman equation and the Kolmogorov forward equation. JEL Classification: C6, D3, D5, E2

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    Bibliographic Info

    Paper provided by European Central Bank in its series Working Paper Series with number 1608.

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    Date of creation: Nov 2013
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    Handle: RePEc:ecb:ecbwps:20131608

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    Related research

    Keywords: calculus of variations; dynamic programming; heterogeneous agents; Kolmogorov forward equation;

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    1. Robert E. Lucas, Jr. & Benjamin Moll, 2011. "Knowledge Growth and the Allocation of Time," NBER Working Papers 17495, National Bureau of Economic Research, Inc.
    2. S. Rao Aiyagari, 1993. "Uninsured idiosyncratic risk and aggregate saving," Working Papers 502, Federal Reserve Bank of Minneapolis.
    3. Stiglitz, Joseph E, 1976. "Monopoly and the Rate of Extraction of Exhaustible Resources," American Economic Review, American Economic Association, vol. 66(4), pages 655-61, September.
    4. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, MIT Press, vol. 122(3), pages 1103-1144, 08.
    5. Pindyck, Robert S, 1980. "Uncertainty and Exhaustible Resource Markets," Journal of Political Economy, University of Chicago Press, vol. 88(6), pages 1203-25, December.
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