A model of financial market with several interacting assets. Complete market case (Q1409836)

A generalization of the multidimensional Black-Scholes financial market model is proposed in which several assets can interact with each other even in the absence of a noise. Sufficient conditions of the existence of an equivalent martingale measure and non-arbitrage are derived. The completeness of the model and pricing of contingent claims are discussed. The associated stochastic differential equation for the stock prices is solved. The results are applied to the pricing of stock index options.