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Martingale conditions for optimal saving: discrete time

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  • Foldes, Lucien

Abstract

Necessary and sufficient conditions are derived for optimal saving in a stochastic neo-classical one-good world with discrete time. The usual technique of dynamic programming is replaced by classical variational and concavity arguments, modified to take account of conditions of measurability which represent the planner's information structure. Familiar conditions of optimality are thus extended to amit production risks represented by quite general random processes - no i.i.d.r.v.s., stationarity or Markov dependence are assumed - while utility and length of life also may be taken as random. It is found that the 'Euler' conditions may be interpreted as martingale properties of shadow prices.

Suggested Citation

  • Foldes, Lucien, 1978. "Martingale conditions for optimal saving: discrete time," LSE Research Online Documents on Economics 3231, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:3231
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    File URL: http://eprints.lse.ac.uk/3231/
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    Cited by:

    1. Kamihigashi, Takashi, 2005. "Necessity of the transversality condition for stochastic models with bounded or CRRA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1313-1329, August.
    2. Foldes, Lucien, 2000. "Valuation and martingale properties of shadow prices: An exposition," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1641-1701, October.
    3. Selby, Michael J. P., 2000. "Computational Aspects of Complex Securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1491-1497, October.
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

    More about this item

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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