Valuation and Martingale properties of shadow prices

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 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 Savin with an exogenous random income and (ii) the use of random time transforms to replace local by true martingales in the martingale and transversatility conditions for optimal saving and portfolio choice.

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