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Valuation and Martingale properties of shadow prices

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  • Foldes, Lucien

Abstract

Concepts of asset valuation based on the martingale properties of shadow (or marginal utility) prices in continuous-time, infinite-horizon stochastic models of optimal saving and portfolio choice are reviewed and compared with their antecedents in static or deterministic economic theory. Applications of shadow pricing to valuation are described, including a new derivation of the Black-Scholes formula and a generalised net present value formula for valuing an indivisible project yielding a random income. Some new results are presented concerning (I) the characterisation of an optimum in a model of saving with an exogenous random income and (ii) the use of random time transforms to replace local by true martingales in the martingale and transversality conditions for optimal saving and portfolio choice.

Suggested Citation

  • Foldes, Lucien, 2000. "Valuation and Martingale properties of shadow prices," LSE Research Online Documents on Economics 5139, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:5139
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    File URL: http://eprints.lse.ac.uk/5139/
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    More about this item

    Keywords

    Valuation; investment; optimisation; continuous time; Martingales; transversality; time change;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory

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