  We perform in-depth dynamical modelling of the luminous and dark matter (DM)
content of the elliptical galaxy NGC 1407. Our strategy consists of solving the
spherical Jeans equations for three independent dynamical tracers: stars, blue
GCs and red GCs in a self-consistent manner. We adopt a maximum-likelihood
Markov-Chain Monte Carlo fitting technique in the attempt to constrain the
inner slope of the DM density profile (the cusp/core problem), and the stellar
initial mass function (IMF) of the galaxy. We find the inner logarithmic slope
of the DM density profiles to be $\gamma = 0.6\pm0.4$, which is consistent with
either a DM cusp ($\gamma = 1$) or with a DM core $(\gamma = 0)$. Our findings
are consistent with a Salpeter IMF, and marginally consistent with a Kroupa
IMF. We infer tangential orbits for the blue GCs, and radial anisotropy for red
GCs and stars. The modelling results are consistent with the virial
mass--concentration relation predicted by $\Lambda$CDM simulations. The virial
mass of NGC 1407 is $\log$ $M_{\rm vir} = 13.3 \pm 0.2 M_{\odot}$, whereas the
stellar mass is $\log M_* = 11.8 \pm 0.1 M_{\odot}$. The overall uncertainties
on the mass of NGC 1407 are only 5 per cent at the projected stellar effective
radius. We attribute the disagreement between our results and previous X-ray
results to the gas not being in hydrostatic equilibrium in the central regions
of the galaxy. The halo of NGC 1407 is found be DM dominated, with a dynamical
mass-to-light ratio of $M/L=260_{-100} ^{+174} M_{\odot}/L_{\odot, B}$.
However, this value can be larger up to a factor of 3 depending on the assumed
prior on the DM scale radius.
