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Valuation and martingale properties of shadow prices: An exposition

Identifieur interne : 000210 ( Main/Exploration ); précédent : 000209; suivant : 000211

Valuation and martingale properties of shadow prices: An exposition

Auteurs : Lucien Foldes [Royaume-Uni]

Source :

RBID : ISTEX:995A6A7991010377C33F115BE49D015F9ED0DA65

English descriptors

Abstract

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.

Url:
DOI: 10.1016/S0165-1889(99)00090-1


Affiliations:


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Le document en format XML

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<term>Necessary conditions</term>
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<term>Nite life</term>
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<term>Riskless security</term>
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<term>Single security</term>
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<term>Special cases</term>
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<term>Standardised units</term>
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<term>Suitable sequence</term>
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<div type="abstract" xml:lang="en">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.</div>
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