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Statistics for Finance by Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen

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Chapter 7

Stochastic calculus

In this and the following chapter, stochastic differential equations will be formally introduced. This exposition to stochastic calculus does not pretend to be complete. The presentation will be guided by intuition, and important topics and results from a practitioner's point of view will covered at a reasonable mathematical level. General measure theory and other technicalities of a (purely) mathematical interest will be kept at a minimum, but the reader is referred to Arnold [1974], Karatzas and Shreve [1996], Ikeda and Watanabe [1989] and Øksendal [2010] for a detailed account. It should be emphasized that the material in this chapter is not only of interest in mathematical finance. To stress the broad applicability, ...

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