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1995•Stochastic Analysis and ApplicationsRequires access

On the minimal martingale measure and the möllmer-schweizer decomposition

Martin Schweizer

Open publisher page 333 citations

Abstract

We provide three characterizations of the minimal martingale measure[Pcirc] associated to a given d-dimensional semimartingale X. In each case, [Pcirc] 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 Föllmer-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[Pcirc] associated to a given d-dimensional semimartingale X. In each case, [Pcirc] 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 Föllmer-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[Pcirc] associated to a given d-dimensional semimartingale X. In each case, [Pcirc] 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 Föllmer-Schweizer decomposition to the case where X is continuous, but multidimensional.

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

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