Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local -martingales. We prove that if exists, it minimizes the reverse relative entropy H(PQ) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.
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