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On the minimal martingale measure and the Föllmer-Schweizer decomposition. (English) Zbl 0837.60042

The concept of equivalent martingale measure for a semimartingale \(X\) is useful in problems related to the absence of arbitrage in stochastic finance. It has first been studied by Föllmer and Schweizer when \(X\) is a real process; in the paper under review, the multidimensional case is investigated. Three characterizations of the minimal martingale measure associated with \(X\) are given, and a previous result of J.-P. Ansel and C. Stricker [Ann. Inst. Henri Poincaré, Probab. Stat. 28, No. 3, 375-392 (1992; Zbl 0772.60033)] concerning the so-called Föllmer- Schweizer decomposition is extended to the multidimensional case.

MSC:

60G44 Martingales with continuous parameter

Citations:

Zbl 0772.60033
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References:

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