Geological faults may produce earthquakes under the increased stresses associated with hydrocarbon recovery, geothermal extraction, CO2 storage. The associated risks depend on the frequency and magnitude of these earthquakes. Within seismic risk analysis, the exceedance probability of seismic moments, Μ, is treated as a pure power-law distribution, Μ^{-β}, where the power-law exponent, β, may vary in time or space or with stress. Insights from statistical mechanics theories of brittle failure, statistical seismology, and acoustic emissions experiments all indicate this pure power-law may contain an exponential taper, Μ^{-β}e^{-ζ Μ}, where the taper strength, ζ, decreases with increasing stress. The role of this taper is to significantly reduce the probability of earthquakes larger than ζ^{-1} relative to the pure power-law. We review the existing theoretical and observational evidence for a stress-dependent exponential taper to motivate a range of magnitude models suitable for induced seismicity risk analysis. These include stress-invariant models with and without a taper, stress-dependent β models without a taper, and stress-dependent ζ models. For each of these models, we evaluated their forecast performance within the Groningen gas field in the Netherlands using a combination of Bayesian inference, and simulations. Our results show that the stress-dependent ζ-model with constant β likely offer (75–85%) higher performance forecasts than the stress-dependent β-models with ζ = 0. This model also lowers the magnitudes with a 10% and 1% chance of exceedance over the next 5 years of gas production from 4.3 to 3.7 and from 5.5 to 4.3 respectively.