Exact Arbitrage and Portfolio Analysis in Large Asset Markets

We provide a detailed portfolio analysis for a nancial market with an atomless continuum of assets. In the context of an exact arbitrage pricing theory (EAPT), we go beyond the characterization of the existence of important portfolios (normalized riskless, mean, cost, factor and mean-variance eÆcient portfolios) to furnish exact portfolio compositions in terms of explicit portfolio weights. Such an analysis has not been furnished before in the context of the asymptotic arbitrage pricing theory (APT). We also characterize conditions under which a mean-variance eÆcient portfolio is a benchmark portfolio used in the EAPT to proxy essential risk. We illustrate our results with several examples of speci c nancial markets.