Minimal Martingale Measure

Abstract

Abstract Suppose discounted asset prices in a financial market are given by aP‐semimartingale of the formS = S0 + M + A. The minimal martingale measure forSis characterized by the properties that it turnsSinto a local martingale and preserves the martingale property for any localP‐martingale stronglyP‐orthogonal toM. It plays a key role in finding locally risk‐minimizing strategies, and it comes up in various other contexts as well. Importantly, its density process can be written explicitly in terms ofMandA, so that one can use it very generally and broadly. In some specific settings, it also has other optimality properties.

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