Étude de peacocks sous l'hypothèse de monotonie conditionnelle et de positivité totale

Abstract : This thesis deals with real valued stochastic processes which increase in the convex order. We call them peacocks. A remarkable result due to Kellerer states that a real valued process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is said to be associated to this process. But in his article, Kellerer provides neither an example of peacock nor a concrete idea to construct an associated martingale to a given peacock. Hence, as other investigations on peacocks, our study has two purposes. We first exhibit new families of peacocks and then, we contruct associated martingales to certain of them. In the first three chapters, we exhibit several classes of peacocks using successively the notions of conditional monotonicity, very strong peacock and total positivity of order 2. In particular, we provide many extensions of Carr-Ewald-Xiao result which states that the arithmetic mean of geometric Brownian motion, also called "Asian option" is a peacock. The purpose of the last chapter is to construct associated martingales to certain peacocks. To this end, we use Azéma-Yor and Bertoin-Le Jan embedding algorithms. The originality of this chapter is the use of total positivity of order 2 in the study of Azéma-Yor embedding algorithm
Document type :
Theses
Complete list of metadatas

Cited literature [67 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01749347
Contributor : Thèses Ul <>
Submitted on : Thursday, March 29, 2018 - 12:13:48 PM
Last modification on : Wednesday, April 11, 2018 - 1:29:28 AM
Long-term archiving on: Friday, September 14, 2018 - 10:33:49 AM

File

DDOC_T_2012_0152_BOGSO.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01749347, version 1

Collections

Citation

Antoine Marie Bogso. Étude de peacocks sous l'hypothèse de monotonie conditionnelle et de positivité totale. Mathématiques générales [math.GM]. Université de Lorraine, 2012. Français. ⟨NNT : 2012LORR0152⟩. ⟨tel-01749347⟩

Share

Metrics

Record views

34

Files downloads

28