The velocity of interstellar asteroid 'Oumuamua with respect to the Local Standard of Rest of our Galaxy is low, which implies it is young, at least if it was ejected during its host star's protoplanetary phase. With this young age as our hypothesis, we assess possible origin systems for the interstellar asteroid in two ways.First, by modelling 'Oumuamua's past trajectory under the influence of the galactic tide and the disk heating (ie. scattering) to assess how far back one can reliably expect to trace its orbit. The stochastic nature of disk heating means that a back integration of 'Oumuamua can only expect to be accurate to within 15 pc and 2 km/s at -10 Myr, 100 pc and 5 km/s at -50 Myr, and 400 pc and 10 km/s at -100 Myr, sharply limiting our ability to determine a precise origin. However, we can show that if 'Oumuamua was ejected at low (∼ 1 km/s) speed, as is likely for most ejection processes, 'Oumuamua's origin system is currently within 1 kpc of Earth. This would place the origin system nearby within the local Orion Arm, and thus relatively easily accessible to telescopic study. This provides strong motivation for continued efforts to determine 'Oumuamua's place of origin, because that system could be studied in detail and shed light on the nature of this unusual asteroid.Second, with this initial assessment in hand, we perform a backwards integration of 'Oumuamua's trajectory accounting for uncertainty in its and the candidate source regions' speed and position where possible, to assess potential candidate regions. The Gaia DR2 catalog and the SIMBAD catalog were considered, with particular emphasis on young systems as detailed in the Catalog of Suspected Nearby Young Stars ) and moving groups as compiled in Gagné et al. (2018). Though disk heating prevents making any but a statistical link to local star-forming regions and moving groups, our best candidates are the Carina and Columba moving groups, the Lupus SFR, the T-Tau stars V391 Ori and BD+11 414, and the M dwarf GJ 1167 A. 'Oumuamua passed through at least a considerable subset of the Carina and Columba moving groups at a time comparable to their ages, making it perhaps the most plausible source region, if the asteroid was ejected by the planet-forming process.During the writing of this paper, a second interstellar comet 2I/Borisov was discovered. Though unlikely to be young due to its high velocity with respect to the LSR, we performed a similar analysis and found three stars in the Ursa Major group (GJ 4384, EV Lac, and GJ 102), one brown dwarf of the AB Dor group (2MASS J03552337+113343), and 8 Gaia DR2 stars (including EV Lac) to have plausible encounters at speeds <30 kms −1 and within 2 pc. We do not find any plausible encounters at speeds lower than 13 kms −1 .