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An analytical model for fully developed three-dimensional incompressible turbulence was recently proposed in the hydrodynamics community, based on the concept of multiplicative chaos. It consists of a random field represented by means of a stochastic integral, which, with only a few parameters, shares many properties with experimental and numerical turbulence, including in particular energy transfer through scales (the cascade) and intermittency (non-Gaussianity) which is most conveniently controlled with a single parameter. Here, we propose three models extending this approach to MHD turbulence. Our formulae provide physically motivated 3D models of a turbulent velocity field and magnetic field coupled together. Besides its theoretical value, this work is meant to provide a tool for observers: a dozen of physically meaningful free parameters enter the description, which is useful to characterize astrophysical data.