The multivariate Black \& Scholes market: conditions for completeness and no-arbitrage (Q2923401)

The paper contains a systematic overview of the basic results concerning the multivariate Black and Scholes asset pricing model. The authors formulate and give a detailed proof of an arbitrage-free condition for such market and establish its completeness. They introduce the assumption supplying the existence of an equivalent description of the multivariate Black and Scholes model in terms of correlated Brownian motions or in terms of a linear combination of independent Brownian motions. Furthermore, it is proved that this special version of the Black and Scholes model is always arbitrage-free and complete.