THE CONTINUOUS-TIME APT WITH DIFFUSION FACTORS AND RATIONAL EXPECTATIONS: A SYNTHESIS

Abstract

The APT is recast as a general theory of arbitrage asset valuation in a model with diffusion factors and rational expectations. Defining betas by factor elasticities of asset prices, the APT-type arbitrage-free condition is reformulated in terms of asset price function. The condition reduces to a partial differential equation with respect to the asset valuation function. The price function, as a solution of this equation, takes two alternative forms depending on how to design risk-adjustment. The resulting formulae consistently demonstrate the various existing ideas of arbitrage asset evaluation.