Characteristic features of chemically induced dynamic electron polarization (CIDEP) in radical pair (RP) recombination in micelles are analyzed theoretically. The confinement effect of micelles is modeled by the spherical stepwise potential well for the radicals. The accurate and rigorous analytical expression for the multiplet CIDEP at long times is derived by solution of the stochastic Liouville equation (SLE) for the RP spin density matrix. It is shown that in the limits of weak and strong hyperfine interactions in the radicals, the rigorous analytical results can be interpreted within the simple exponential models which are called the cage and supercage models, respectively. These models enable us to reduce the complicated SLE describing diffusive motion of radicals within the potential well to the Bloch-type equations. The cage and supercage models are applied to the analysis of the CIDEP generation kinetics and the electron-spin resonance (ESR) line shape of spin correlated RPs in micelles. The models make it possible to predict simple relations of characteristic parameters of kinetics and the line shape with the parameters of the general problem: diffusion coefficients, the size and depth of the potential well, etc.