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2010•Journal of National University of Defense TechnologyRequires access

On the Semi-martingale Predictable Representation

Jin Zhi-ming

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Abstract

The characteristics for semi-martingale predictable representation are obtained(theorem2.2),which is derived from the functional representation theorem in martingale space,the Hahn-Banach theorem in functional analysis,and the Girsanov theorem for the semi-martingale vector stochastic integral.In light of the semi-martingale vector stochastic integral used,this method is a generalization of the classical result.

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What this paper is about

The characteristics for semi-martingale predictable representation are obtained(theorem2.2),which is derived from the functional representation theorem in martingale space,the Hahn-Banach theorem in functional analysis,and the Girsanov theorem for the semi-martingale vector stochastic integral.In light of the semi-martingale vector stochastic integral used,this method is a generalization of the classical result.

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Available abstract

The characteristics for semi-martingale predictable representation are obtained(theorem2.2),which is derived from the functional representation theorem in martingale space,the Hahn-Banach theorem in functional analysis,and the Girsanov theorem for the semi-martingale vector stochastic integral.In light of the semi-martingale vector stochastic integral used,this method is a generalization of the classical result.

Key concepts: Mathematics, Martingale (probability theory), Martingale difference sequence, Local martingale, Martingale representation theorem, Girsanov theorem, Martingale pricing, Representation theorem

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