We provide a self-contained analysis of a class of continuous-time stochastic mortality models that have gained popularity in the last few years. We describe some of their advantages and limitations, examining whether their features survive equivalent changes of measures. This is important when using the same model for both market-consistent valuation and risk management of life insurance liabilities. We provide a numerical example based on the calibration to the French annuity market of a risk-neutral version of the model proposed by Lee and Carter (1992).