ニューメレールの使い方

I fail to understand the reasoning behind the change of numeraire in the derivation of the Libor Market Model forward rate process, nor do I see where the v(m)-v(k) factor arises from. やっぱり先物の利子と債券の割引因数の関係がニューメレールの原因です。The forward rate can be expressed as the ratio of the risk-free rate and the bond discount factor P(t,tk+1). Thus P(t,tk+1) is the numeraire, and the initial forward rate process is forward risk neutral with respect to P(t,tk+1). Thus, the dF process is a Martingale and has 0 drift. (Corrected, see below) However, the forward process is redefined, out of convenience, in terms of the bond discount factor for the next maturity date, P(t,m(t)). The dF process would not be a martingale with this new numeraire. The change of numeraire formula is defined by expressing drift=r+lambda*sigma. By changing numeraire from P(t,tk+1) to P(t,tm), we are changing lambda from v(k+1) to v(m), and thus, the drift of F increases by (vm-vk+1)*xi(k) where xi is thevolatility of F. Two points are still 不明。1. Why the volatility of P(t,tm) can be taken to be the market price of risk. (Seems to be that the definition of the world we consider is the risk tolerance). 2. Why the forward process with P(t,tm) is not a martingale (seems to be because we use same Brownian Motion and probability measure in both expressions, and, if a new probability distribution is used, it would be). 3. If F is not defined in terms of r/P, then how is F a martingale?
It seems that the original dF is a Martingale not because it is written as r/P, but because F =1/P-1, so, if P is a Martingale, then so is F. 訂正
In fact the original notion of expressing the forward rate as a ratio with P as the denominator, hence the numeraire, was correct. The ratio is a Martingale in a forward risk neutral world wrt P. However, the formula is: (Hull) R(t,T1,T2)=(1/(T2-T1))(P(t,T1)-P(t,T2))/P(t,T2). Let x=(1/(T2-T1))(P(t,T1)-P(t,T2)), and y=P(t,T2), then x/y is a Msrtingale,