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Valuation and Martingale Properties of Shadow Prices

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  • Lucien Foldes

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.This paper was also published in the ¶Journal of Economic Dynamics and Control¶ #24 (2000). Pages 1641-1701.

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  • Lucien Foldes, 2000. "Valuation and Martingale Properties of Shadow Prices," FMG Discussion Papers dp342, Financial Markets Group.
    • Handle: RePEc:fmg:fmgdps:dp342
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    Cited by:

    1. Rosen, H.S.Harvey S. & Wu, Stephen, 2004. "Portfolio choice and health status," Journal of Financial Economics, Elsevier, vol. 72(3), pages 457-484, June.
    2. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2017. "An indifference approach to the cost of capital constraints: KVA and beyond," Papers 1708.05319, arXiv.org.
    3. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    4. Harvey S. Rosen & Stephen Wu, 2001. "Health Status and Portfolio Choice," Working Papers 127, Princeton University, Department of Economics, Center for Economic Policy Studies..
    5. Harvey S. Rosen & Stephen Wu, 2001. "Health Status and Portfolio Choice," Working Papers 127, Princeton University, Department of Economics, Center for Economic Policy Studies..
    6. Kallsen Jan & Kühn Christoph, 2006. "On utility-based derivative pricing with and without intermediate trades," Statistics & Risk Modeling, De Gruyter, vol. 24(4/2006), pages 1-20, October.

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