A minimality property of the minimal martingale measure

Martin Schweizer

No 1998,106, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: 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.

Keywords: relative entropy; minimal martingale measure; equivalent martingale measures (search for similar items in EconPapers)
JEL-codes: G10 (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:1998106

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