Am I correct in saying that there can only be 1 model for mortality? From CT4, I remember that the probability density function for Tx is tPxUx+t and the Ux's are paremeters in this pdf.
Mortality can either (mainly) modelled with the Poisson or Binomial models. This isn't (to my understanding) the main cause of "modelling risk". Modelling Risk is mainly due to not splitting the rates between appropriate causal parameters, such as Gender, Smoker status, Health etc. If this data is available (ie via underwriting), and relevent, then it should be used in Pricing. Parameter risk then follows from not parametrizing these models correctly (eg getting the age adjustments incorrect).
In addition to the three models you two have mentioned so far, CT4 also covers (in a big way) the Markov jump process model for mortality, where you have two states (alive and dead) and transitions occur between A and D at annual rate (mu)x at any given age x. But as Rosencruz says, which of these models you "use" makes very little difference in practice - it's the allowance (or otherwise) for the other factors that can lead to significant modelling error.
