On the relationship of the dynamic programming approach and the contingent claim approach to asset valuation

We consider a general model for an investment producing a single commodity, and, assuming that there exists a traded asset spanning the corresponding market, we prove a "verification theorem" which relates the solution of an appropriate differential equation with the investment's contingent claim price. In this way, we show in a mathematically rigorous way that the contingent claim approach and the dynamic programming approach to the problem of asset valuation are equivalent, modulo parameter calibration. Our analysis can be used in a straightforward way to address a big number of investment models.