Existence of Pseudo-Inverses for Diffusions

Christophe Profeta (), Bernard Roynette () and Marc Yor
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Christophe Profeta: Université Nancy I
Bernard Roynette: Université Nancy I
Marc Yor: Université Paris VI

Chapter Chapter 8 in Option Prices as Probabilities, 2010, pp 203-237 from Springer

Abstract: Abstract In this chapter, we continue the study of pseudo-inverses, extending the previous results of Chapter 7 to the general framework of linear diffusions. We shall focus here on increasing pseudo-inverses, and we shall deal with two cases: first, a diffusion taking values in ℝ, and solution of a particular SDE, and then, a general diffusion on ℝ+ starting from 0. More precisely, we shall prove that, to a positive diffusion X starting from 0, we can associate another diffusion $\overline{X}$ such that the tail probabilities of X are the distribution functions of the last passage times of $\overline{X}$ .

Date: 2010
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DOI: 10.1007/978-3-642-10395-7_8

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