This paper introduces an straightforward algorithm to determine a range of prices consistent with complete information about the risk but only partial information about the pricing risk measure. In many cases the algorithm produces bounds tight enough to be useful in practice. The paper illustrates the theory by applying it to two important problems: pricing for high limits relative to low limits (which applies to evaluating reinsurance programs) and portfolio-level strategic decision making. It also shows how the theory can be used to test if prices for known risks are consistent with a single partially specified risk measure.

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