Before revision:  We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly,  all the moments of order greater than one are infinite.
After revision:  We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly, then, for the asset price process, all the moments of order greater than one are infinite.