There are many situations that we need to model as risky prospects whose values are censored below at 0, hence defined on semi-infinite support. As useful tools for such models, we derive analytic characterizations of risks such as certainty equivalent and risk premium, for gamma and lognormal distributions and utility functions that have constant risk aversion. As a main application, we consider an extension of the `linear contract, exponential utility, normally distributed risks' (LEN) moral hazard model to gamma distributed risks. We also discuss other potential applications, ranging from loan contracts to comparison of income distributions.