We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent...

This paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one-dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This...