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

A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and completeness are given. In the case of a complete market the pricing of contingent claims based on several assets (e.g. index options) is considered and explicit formulas are derived.