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Discounted dynamic optimization and Bregman divergence

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  • Sorger, Gerhard

Abstract

We define the concept of Bregman continuity and show that a function is an optimal policy function of a discounted dynamic optimization problem if and only if it is Bregman continuous.

Suggested Citation

  • Sorger, Gerhard, 2024. "Discounted dynamic optimization and Bregman divergence," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    • Handle: RePEc:eee:mateco:v:110:y:2024:i:c:s0304406823001283
    DOI: 10.1016/j.jmateco.2023.102935
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    References listed on IDEAS

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    1. Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
    2. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    3. Gerhard Sorger, 2006. "Rationalizability in Optimal Growth Theory," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 4, pages 85-113, Springer.
    4. M. Kurz, 1971. "The General Instability of a Class of Competitive Growth Processes," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 17, pages 218-237, Palgrave Macmillan.
    5. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    6. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    7. Sorger, Gerhard, 1992. "On the minimum rate of impatience for complicated optimal growth paths," Journal of Economic Theory, Elsevier, vol. 56(1), pages 160-179, February.
    8. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    9. Tapan Mitra & Gerhard Sorger, 1999. "On the Existence of Chaotic Policy Functions in Dynamic Optimization," The Japanese Economic Review, Japanese Economic Association, vol. 50(4), pages 470-484, December.
    10. Tapan Mitra & Kazuo Nishimura & Gerhard Sorger, 2006. "Optimal Cycles and Chaos," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 6, pages 141-169, Springer.
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