Existence and Properties of Pseudo-Inverses for Bessel and Related Processes

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 7 in Option Prices as Probabilities, 2010, pp 161-201 from Springer

Abstract: Abstract In Chapter 6, we have shown the existence of a decreasing pseudo-inverse for the martingale $(M_{t}:=\exp\left(B_{t}-\frac{t}{2}\right),t\geq0)$ . We shall now explore this notion in a more general framework, starting with the case of Bessel (and some related) processes. We show in particular that the tail probabilities of a Bessel process of index ν≥1/2 increase with respect to time; in fact it is the distribution function of a random time which is related to first and last passage times of Bessel processes.

Date: 2010
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DOI: 10.1007/978-3-642-10395-7_7

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