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Reverse Calculus and nested optimization

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  • Clausen, Andrew
  • Strub, Carlo

Abstract

Nested optimization problems arise when an agent must take into account the effect of their decisions on their own future behaviour, or the behaviour of others. In these problems, calculating marginal costs and benefits involves differentiating the solutions to nested problems. But are these solutions differentiable functions? We develop a tool called Reverse Calculus, and establish first-order conditions for (i) a Stackelberg leader considering the follower's best response function, (ii) a sovereign borrower considering its own future default policy, and (iii) non-convex dynamic programming problems.

Suggested Citation

  • Clausen, Andrew & Strub, Carlo, 2020. "Reverse Calculus and nested optimization," Journal of Economic Theory, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jetheo:v:187:y:2020:i:c:s0022053120300247
    DOI: 10.1016/j.jet.2020.105019
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    Cited by:

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    2. Youngsoo Jang & Soyoung Lee, 2021. "A Generalized Endogenous Grid Method for Default Risk Models," Staff Working Papers 21-11, Bank of Canada.
    3. Le Grand, François & Ragot, Xavier, 2021. "Sovereign default and liquidity: The case for a world safe asset," Journal of International Economics, Elsevier, vol. 131(C).
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    5. Damián Pierri & Hernán D. Seoane, 2022. "An Ergodic Theory of Sovereign Default," Working Papers 206, Red Nacional de Investigadores en Economía (RedNIE).
    6. Jang, Youngsoo & Lee, Soyoung, 2019. "A Generalized Endogenous Grid Method for Models with the Option to Default," MPRA Paper 95721, University Library of Munich, Germany.
    7. Alexandre Janiak & Jonathan Rojas Hepburn, 2023. "The Grasshopper, the Ant, and the Minimum Wage," Documentos de Trabajo 570, Instituto de Economia. Pontificia Universidad Católica de Chile..
    8. Ludvig Sinander, 2022. "The Converse Envelope Theorem," Econometrica, Econometric Society, vol. 90(6), pages 2795-2819, November.
    9. Youngsoo Jang, 2023. "Credit, Default, And Optimal Health Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 943-977, August.
    10. repec:hal:wpspec:info:hdl:2441/3jhmd4ib388m99gnolvi8klga2 is not listed on IDEAS
    11. Simon Naitram, 2022. "How big are strategic spillovers from corporate tax competition?," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 847-869, April.

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    More about this item

    Keywords

    First-order conditions; Non-convex dynamic programming; Stackelberg problems; Unsecured credit;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • F34 - International Economics - - International Finance - - - International Lending and Debt Problems
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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