Girsanov’s Theorem

Gopinath Kallianpur and Rajeeva L. Karandikar
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Gopinath Kallianpur: University of North Carolina, Department of Statistics
Rajeeva L. Karandikar: Indian Statistical Institute, Department of Mathematics & Statistics

Chapter 5 in Introduction to Option Pricing Theory, 2000, pp 95-101 from Springer

Abstract: Abstract An important issue in mathematical finance is that of putting conditions on a semimartingale X (defined on (Ω, F, P)) which ensure the existence of a probability measure Q equivalent to P such that X is a local martingale on (Ω, F, Q) We will discuss this in detail in later chapters. Here, we will consider probability measures Q equivalent to P, and show that in general, X is a semimartingale on (Ω, F, Q) as well. Also, one can obtain the decomposition of the semimartingale X on (Ω, F, Q) into a Q-local martingale N and a process with bounded variation paths B, and relate N, B to M, A, where X = X0 + M + A is the decomposition of X on (Ω, F, P) into a P-local martingale M and a process with bounded variation paths A. The classical Girsanov’s theorem is a consequence of this.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0511-1_5

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DOI: 10.1007/978-1-4612-0511-1_5

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