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Optimal control with heterogeneous agents in continuous time


  • Nuño, Galo


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

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    References listed on IDEAS

    1. 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.
    2. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 122(3), pages 1103-1144.
    3. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 659-684.
    4. Pindyck, Robert S, 1980. "Uncertainty and Exhaustible Resource Markets," Journal of Political Economy, University of Chicago Press, vol. 88(6), pages 1203-1225, December.
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    More about this item


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

    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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