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Valuation and Martingale properties of shadow prices

Foldes, Lucien (2000) Valuation and Martingale properties of shadow prices. Financial Markets Group Discussion Papers (342). Financial Markets Group, The London School of Economics and Political Science, London, UK.

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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.

Item Type: Monograph (Discussion Paper)
Official URL: https://www.fmg.ac.uk/
Additional Information: © 2000 The Author
Divisions: Systemic Risk Centre
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
JEL classification: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
D - Microeconomics > D9 - Intertemporal Choice and Growth
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
D - Microeconomics > D4 - Market Structure and Pricing > D46 - Value Theory
Date Deposited: 29 May 2008 13:18
Last Modified: 25 Oct 2022 13:06
URI: http://eprints.lse.ac.uk/id/eprint/5139

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