- 2016 IEEE. We consider multi-robot teams operating in uncertain dynamic settings where the costs used for computing task-allocations are not known exactly. In such cases, the desire to minimize the team's expected cost might need to be curtailed if, in doing so, the risk that results is intolerable. We describe a parameterizable variant of the assignment problem that enables a designer to express such preferences, allowing one to take a risk-averse position if the problem demands it. We consider costs that are random variables, but which need not be independent - a useful setting because it permits one to represent inter-robot couplings. We analyze the sensitivity of assignment optima to particular risk valuations and introduce algorithms that provide an interval for the preference parameter in which all values result in the same optimal assignment. This helps in understanding the effects of risk on the problem, and whether the risk-based model is useful in a given problem domain.