Dissertation/ Thesis
Προβολή σε EDS

A study of Peacocks under the assumptions of conditional monotonicity and total positivity

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: A study of Peacocks under the assumptions of conditional monotonicity and total positivity
Συγγραφείς: Bogso, Antoine Marie
Συνεισφορές: UL, Thèses
Στοιχεία εκδότη: 2012.
Έτος έκδοσης: 2012
Θεματικοί όροι: Conditional monotonicity, Positivité totale d'ordre 2, Monotonie conditionnelle, Plongement de Bertoin-Le Jan, Markov processes, Martingales (mathématiques), [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Probabilités, Mouvement brownien, Plongement d'Azéma-Yor, Azéma-Yor algorithm for Skorokhod embedding, Peacocks, Martingales, Processus de Markov, Stochastic processes, Processus stochastiques, Markov, Skorokhod embedding problem, Brownian motion, Total positivity of order 2, Bertoin-Le Jan solution for Skorokhod embedding, Problème de Skorokhod, Processus de
Περιγραφή: Cette thèse porte sur les processus croissants pour l'ordre convexe que nous désignons sous le nom de peacocks. Un résultat remarquable dû à Kellerer stipule qu'un processus stochastique à valeurs réelles est un peacock si et seulement s'il possède les mêmes marginales unidimensionnelles qu'une martingale. Une telle martingale est dite associée à ce processus. Mais dans son article, Kellerer ne donne ni d'exemple de peacock, ni d'idée précise sur la construction d'une martingale associée pour un peacock donné. Ainsi, comme d'autres travaux sur les peacocks, notre étude vise deux objectifs. Il s'agit d'exhiber de nouvelles familles de peacocks et de construire des martingales associées pour certains peacocks. Dans les trois premiers chapitres, nous exhibons diverses classes de peacocks en utilisant successivement les notions de monotonie conditionnelle, de peacock très fort et de positivité totale d'ordre 2. En particulier, nous fournissons plusieurs extensions du résultat de Carr-Ewald-Xiao selon lequel la moyenne arithmétique du mouvement brownien géométrique, encore appelée "option asiatique" est un peacock. L'objet du dernier chapitre est de construire des martingales associées pour une classe de peacocks. Pour cela, nous utilisons les plongements d'Azéma-Yor et de Bertoin-Le Jan. L'originalité de ce chapitre est l'utilisation de la positivité totale d'ordre 2 dans l'étude du plongement d'Azéma-Yor
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
Τύπος εγγράφου: Doctoral thesis
Περιγραφή αρχείου: application/pdf
Γλώσσα: French
Σύνδεσμος πρόσβασης: https://hal.univ-lorraine.fr/tel-01749347v1
Αριθμός Καταχώρησης: edsair.a9ac50f576aa..ae077f32d45867aad2c18fb2c36e7f3f
Βάση Δεδομένων: OpenAIRE
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  Data: A study of Peacocks under the assumptions of conditional monotonicity and total positivity
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  Data: UL, Thèses
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  Label: Publisher Information
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  Data: 2012.
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  Label: Publication Year
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  Data: 2012
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Conditional+monotonicity%22">Conditional monotonicity</searchLink><br /><searchLink fieldCode="DE" term="%22Positivité+totale+d'ordre+2%22">Positivité totale d'ordre 2</searchLink><br /><searchLink fieldCode="DE" term="%22Monotonie+conditionnelle%22">Monotonie conditionnelle</searchLink><br /><searchLink fieldCode="DE" term="%22Plongement+de+Bertoin-Le+Jan%22">Plongement de Bertoin-Le Jan</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Martingales+%28mathématiques%29%22">Martingales (mathématiques)</searchLink><br /><searchLink fieldCode="DE" term="%22[MATH%2EMATH-GM]+Mathematics+[math]%2FGeneral+Mathematics+[math%2EGM]%22">[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]</searchLink><br /><searchLink fieldCode="DE" term="%22Probabilités%22">Probabilités</searchLink><br /><searchLink fieldCode="DE" term="%22Mouvement+brownien%22">Mouvement brownien</searchLink><br /><searchLink fieldCode="DE" term="%22Plongement+d'Azéma-Yor%22">Plongement d'Azéma-Yor</searchLink><br /><searchLink fieldCode="DE" term="%22Azéma-Yor+algorithm+for+Skorokhod+embedding%22">Azéma-Yor algorithm for Skorokhod embedding</searchLink><br /><searchLink fieldCode="DE" term="%22Peacocks%22">Peacocks</searchLink><br /><searchLink fieldCode="DE" term="%22Martingales%22">Martingales</searchLink><br /><searchLink fieldCode="DE" term="%22Processus+de+Markov%22">Processus de Markov</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Processus+stochastiques%22">Processus stochastiques</searchLink><br /><searchLink fieldCode="DE" term="%22Markov%22">Markov</searchLink><br /><searchLink fieldCode="DE" term="%22Skorokhod+embedding+problem%22">Skorokhod embedding problem</searchLink><br /><searchLink fieldCode="DE" term="%22Brownian+motion%22">Brownian motion</searchLink><br /><searchLink fieldCode="DE" term="%22Total+positivity+of+order+2%22">Total positivity of order 2</searchLink><br /><searchLink fieldCode="DE" term="%22Bertoin-Le+Jan+solution+for+Skorokhod+embedding%22">Bertoin-Le Jan solution for Skorokhod embedding</searchLink><br /><searchLink fieldCode="DE" term="%22Problème+de+Skorokhod%22">Problème de Skorokhod</searchLink><br /><searchLink fieldCode="DE" term="%22Processus+de%22">Processus de</searchLink>
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  Data: Cette thèse porte sur les processus croissants pour l'ordre convexe que nous désignons sous le nom de peacocks. Un résultat remarquable dû à Kellerer stipule qu'un processus stochastique à valeurs réelles est un peacock si et seulement s'il possède les mêmes marginales unidimensionnelles qu'une martingale. Une telle martingale est dite associée à ce processus. Mais dans son article, Kellerer ne donne ni d'exemple de peacock, ni d'idée précise sur la construction d'une martingale associée pour un peacock donné. Ainsi, comme d'autres travaux sur les peacocks, notre étude vise deux objectifs. Il s'agit d'exhiber de nouvelles familles de peacocks et de construire des martingales associées pour certains peacocks. Dans les trois premiers chapitres, nous exhibons diverses classes de peacocks en utilisant successivement les notions de monotonie conditionnelle, de peacock très fort et de positivité totale d'ordre 2. En particulier, nous fournissons plusieurs extensions du résultat de Carr-Ewald-Xiao selon lequel la moyenne arithmétique du mouvement brownien géométrique, encore appelée "option asiatique" est un peacock. L'objet du dernier chapitre est de construire des martingales associées pour une classe de peacocks. Pour cela, nous utilisons les plongements d'Azéma-Yor et de Bertoin-Le Jan. L'originalité de ce chapitre est l'utilisation de la positivité totale d'ordre 2 dans l'étude du plongement d'Azéma-Yor<br />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
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: French
    Subjects:
      – SubjectFull: Conditional monotonicity
        Type: general
      – SubjectFull: Positivité totale d'ordre 2
        Type: general
      – SubjectFull: Monotonie conditionnelle
        Type: general
      – SubjectFull: Plongement de Bertoin-Le Jan
        Type: general
      – SubjectFull: Markov processes
        Type: general
      – SubjectFull: Martingales (mathématiques)
        Type: general
      – SubjectFull: [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]
        Type: general
      – SubjectFull: Probabilités
        Type: general
      – SubjectFull: Mouvement brownien
        Type: general
      – SubjectFull: Plongement d'Azéma-Yor
        Type: general
      – SubjectFull: Azéma-Yor algorithm for Skorokhod embedding
        Type: general
      – SubjectFull: Peacocks
        Type: general
      – SubjectFull: Martingales
        Type: general
      – SubjectFull: Processus de Markov
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Processus stochastiques
        Type: general
      – SubjectFull: Markov
        Type: general
      – SubjectFull: Skorokhod embedding problem
        Type: general
      – SubjectFull: Brownian motion
        Type: general
      – SubjectFull: Total positivity of order 2
        Type: general
      – SubjectFull: Bertoin-Le Jan solution for Skorokhod embedding
        Type: general
      – SubjectFull: Problème de Skorokhod
        Type: general
      – SubjectFull: Processus de
        Type: general
    Titles:
      – TitleFull: A study of Peacocks under the assumptions of conditional monotonicity and total positivity
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            – D: 01
              M: 01
              Type: published
              Y: 2012
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