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1994•RePEc: Research Papers in EconomicsRequires access

On the Minimal Martingale Measure and the Foellmer- Schweizer Decomposition

Martin Schweizer

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Abstract

We provide three characterizations of the minimal martingale measure P associated to a given d- dimensional semimartingale X. In each case, P is shown to be the unique solution of an optimization problem where one minimizes a certain functional over a suitable class of signed local martingale measures for X. Furthermore, we extend a result of Ansel and Stricker on the Foellmer-Schweizer decomposition to the case where X is continuous, but multidimensional.

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What this paper is about

We provide three characterizations of the minimal martingale measure P associated to a given d- dimensional semimartingale X. In each case, P is shown to be the unique solution of an optimization problem where one minimizes a certain functional over a suitable class of signed local martingale measures for X. Furthermore, we extend a result of Ansel and Stricker on the Foellmer-Schweizer decomposition to the case where X is continuous, but multidimensional.

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Available abstract

We provide three characterizations of the minimal martingale measure P associated to a given d- dimensional semimartingale X. In each case, P is shown to be the unique solution of an optimization problem where one minimizes a certain functional over a suitable class of signed local martingale measures for X. Furthermore, we extend a result of Ansel and Stricker on the Foellmer-Schweizer decomposition to the case where X is continuous, but multidimensional.

Key concepts: Semimartingale, Martingale (probability theory), Local martingale, Martingale pricing, Doob's martingale inequality, Mathematics, Martingale difference sequence, Measure (data warehouse)

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