Complements on Continuous Path Processes

Monique Jeanblanc (), Marc Yor and Marc Chesney
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Monique Jeanblanc: Université d’Evry
Marc Yor: Université Paris VI
Marc Chesney: Universität Zürich

Chapter 5 in Mathematical Methods for Financial Markets, 2009, pp 259-332 from Springer

Abstract: Abstract In this chapter, we present the important notion of time change, which will be crucial when studying applications to finance in a Lévy process setting. We then introduce the operation of dual predictable projection, which will be an important tool when working with the reduced form approach in the default risk framework (of course, it has many other applications as will appear clearly in subsequent chapters). We present important facts about general homogeneous diffusions, in particular concerning their Green functions, scale functions and speed measures. These three quantities are of great interest when valuing options in a general setting. We study applications related to last passage times. A section is devoted to enlargements of filtrations, an important subject when dealing with insider trading.

Keywords: Brownian Motion; Inside Trading; Local Martingale; Predictable Process; Bessel Process (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-1-84628-737-4_5

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