2006-03-16Buch DOI: 10.18452/3780
A Minimality Property of the Minimal Martingale Measure
Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P 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 P-martingales. We prove that if P exists, it minimizes the reverse relative entropy H(P|Q) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped.
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