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  risk-neutral measure
A bubble is defined to be a price process which, when discounted, is a local martingale under the risk-neutral measure but not a martingale.
      
We consider a model for interest rates where the short rate is given under the risk-neutral measure by a time-homogeneous one-dimensional affine process in the sense of Duffie, Filipovi?, and Schachermayer.
      
We prove necessary and sufficient conditions in terms of parameters for the existence of an equivalent risk-neutral measure, i.e., a measure under which each asset return has zero expected value.
      
The typical approach used by the industry, which involves simulating interest rates under the risk-neutral measure and applying a physically measured prepayment function, is subject to the problem of internal inconsistency.
      
A time-dependent drift is applied to the credit quality process in order to change to a risk-neutral measure.
      
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  risk neutral measure
This choice may be dependent by agents' preferences and it is related to some risk neutral measure.
      
There are several methods that exploit the representation of the price as the expected payoff under the risk neutral measure.
      
These methods exploit the representation of the price as the expected pay-off under the risk neutral measure.
      
These are defined in Section 2 for both the reference probability measure P and a risk neutral measure Q.
      
The expectation is taken with respect to the so cded risk neutral measure.
      
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