State prices find immediate application as a conceptual tool ("contingent claim analysis");[1] but can also be applied to valuation problems.[13] Given the pricing mechanism described, one can decompose the derivative value — true in fact for "every security" [3] — as a linear combination of its state-prices; i.e. back-solve for the state-prices corresponding to observed derivative prices.[4][13] These recovered state-prices can then be used for valuation of other instruments with exposure to the underlyer, or for other decision making relating to the underlyer itself.