I've just been studying the modelling chapter and wanted to know what is the difference between a parameter, variable and assumption?
It depends whether you are looking at a deterministic or stochastic model. In a deterministic model, the Core Reading is using the word "variable" to mean the thing that you vary until you meet your objective. So, for example, if the objective is to set the premium so that a particular profit criterion is met, then the variable is the premium. You try lots of different premiums, until you hit the one which gives the correct profit criterion. A bit like the function "goal seek" in Excel. Parameters refer to the assumptions, things like mortality, expenses, investment returns, withdrawals, tax rates, reserving assumptions etc. In a stochastic model, the Core Reading uses the word "variable" to refer to any assumption. You have deterministic variables and stochastic variables. The stochastic variables are random and they are modelled with a distribution (pdf) with parameters (eg mu, sigma ...). Nice and confusing.
