The Large Observatory For X-ray Timing (LOFT), currently in an assessment phase in the framework the ESA M3 Cosmic Vision programme, is an innovative medium-class mission specifically designed to answer fundamental questions about the behaviour of matter, in the very strong gravitational and magnetic fields around compact objects and in supranuclear density conditions. Having an effective area of ~10 m^2 at 8 keV, LOFT will be able to measure with high sensitivity very fast variability in the X-ray fluxes and spectra. A good knowledge of the in-orbit background environment is essential to assess the scientific performance of the mission and optimize the design of its main instrument, the Large Area Detector (LAD). In this paper the results of an extensive Geant-4 simulation of the instrument will be discussed, showing the main contributions to the background and the design solutions for its reduction and control. Our results show that the current LOFT/LAD design is expected to meet its scientific requirement of a background rate equivalent to 10 mCrab in 2-30 keV, achieving about 5 mCrab in the most important 2-10 keV energy band. Moreover, simulations show an anticipated modulation of the background rate as small as 10% over the orbital timescale. The intrinsic photonic origin of the largest background component also allows for an efficient modelling, supported by an in-flight active monitoring, allowing to predict systematic residuals significantly better than the requirement of 1%, and actually meeting the 0.25% science goal.
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