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Optimal control with heterogeneous agents in continuous time

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  • Nuño, Galo

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

Suggested Citation

  • Nuño, Galo, 2013. "Optimal control with heterogeneous agents in continuous time," Working Paper Series 1608, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:20131608
    Note: 2253012
    as

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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp1608.pdf
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    References listed on IDEAS

    as
    1. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    2. Pindyck, Robert S, 1980. "Uncertainty and Exhaustible Resource Markets," Journal of Political Economy, University of Chicago Press, vol. 88(6), pages 1203-1225, December.
    3. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    4. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    5. Stiglitz, Joseph E, 1976. "Monopoly and the Rate of Extraction of Exhaustible Resources," American Economic Review, American Economic Association, vol. 66(4), pages 655-661, September.
    6. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    calculus of variations; dynamic programming; heterogeneous agents; Kolmogorov forward equation;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D3 - Microeconomics - - Distribution
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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