<t>Well, intuitively, I would say that, if the 'shifted price process', namely (S(t)+c) (with c the deterministic shift), is lognormal with a lognormal stochastic volatility and, if the correlation is positive, then the 'shifted price process' (S(t)+c) is a supermartingale, i.e. E[S(t)+c|Filtration(...