派生証券の価値を図る確率世界

最近確率と金融工学の方法を考えながら悩んでいます。It is difficult to decipher the relationship between "risk neutral world", "equivalent Martingale measure", and "market price of risk". My understanding is that, in a world where the stochastic component of the return process follows a risk-neutral probability distribution, the drift of the process is the risk-free rate. In addition, a derivative f whose market price of risk equals the volatility of a certain numeraire g such that the numeraire is derived from the same source of uncertainty and E(f/g) is a martingale is said to be valued in a risk neutral world. However, when the drift is r, the market price of risk should be zero. This apparent contradiction is due to the distinction between the traditional risk-neutral world (mkt price of risk is r) and the forward risk-neutral world (mkt price of risk is g's volatility). The Equivalent Martingale Theorem states that there exists g such that for all f, E(ft/gt)=E(f0/g0) (definition of a Martingale).