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## Absolutely Continuous Compensators (2010)

Citations: | 3 - 0 self |

### Citations

68 |
Grossissement initial, hypothese (H ′) et theoreme de Girsanov. In: Grossissements de filtrations: exemples et applications,
- Jacod
- 1985
(Show Context)
Citation Context ...tance recently in the theory of Credit Risk is that of the Expansion of Filtrations. See, for example, [2], [6], or [19]. In the case of initial expansions, we can expand using Jacod’s criterion (see =-=[14]-=- or [26, p. 371]) by adding a random variable L to the filtration F at time 0, provided that for each t ≥ 0 the (regular) conditional distribution of L given Ft, denoted Υt(ω, dx), is such that Υt(ω, ... |

51 | Modeling credit risk with partial information, Working paper, Cornell University, forthcoming, Annals of Applied Probability. - Cetin, Jarrow, et al. - 2003 |

48 | Structural Versus Reduced Form Models: A New Information Based Perspective
- Jarrow, Protter
- 2004
(Show Context)
Citation Context ... in the work of X. Guo and Y. Zeng [12], and examples of intensities arising in the field of Credit Risk can be found there and in their references, as well as in [11] and [18], for example. See also =-=[17]-=-. Examples of intensities arising in the field of Survival Analysis can be found in the book of Fleming and Harrington [9]. Corollary 10 Let X = (Ω, X, P µ) be a semimartingale Hunt process with a Lév... |

30 |
The Brownian escape process
- Getoor
- 1979
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Citation Context ... a given finite set F , sup{t < τ1 : Bt = 0} with τ1 = inf{t > 0 : Bt = 1}, and sup{t : |B (3) t | ≥ 1} where B (3) is a threedimensional Brownian motion and thus |B(3)| is a BES(3) process (see also =-=[10]-=- for this exit time). The results above are easily extended by induction to the case of the filtration F {L1 ,L 2 ,... } extended by a finite or infinite, strictly increasing sequence (Ln) N n=1 of po... |

26 | Limit Theorems for - JACOD, SHIRYAEV - 2003 |

18 |
Point process theory and applications. Marked point and piecewise deterministic processes. Probability and its Applications. Birkhäuser
- Jacobsen
- 2006
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Citation Context ...for a smaller filtration it also has an absolutely continuous compensator in the smaller filtration. Actually one can obtain a more precise result, which is established in the book of Martin Jacobsen =-=[13]-=-. We provide here an original and elementary proof of this result, and inter alia we extend the result a little. Theorem 3 Let R be a G stopping time with compensator given by ∫ t 0 λsdc(s) for some G... |

16 |
Systèmes de Lévy des processus de Markov
- Benveniste, Jacod
- 1973
(Show Context)
Citation Context ... has already been a time change, if necessary, to arrive at a Poisson random measure with compensator ds ν(dx). Here we are not making that assumption. The results contained in (for example) [23] and =-=[3]-=- show that for the additive functional H of the Lévy system, any representation such as (11) must have that the compensator of the corresponding “Poisson random measure” will be absolutely continuous ... |

16 | Intensity process and compensator: A new filtration expansion approach and the Jeulin-Yor theorem.
- Guo, Zeng
- 2008
(Show Context)
Citation Context ...d sufficient conditions. The same proof plus a use of Lévy systems can provide this result, given in Theorem 10. The connection to Lévy systems was recently recalled in the work of X. Guo and Y. Zeng =-=[12]-=-, and examples of intensities arising in the field of Credit Risk can be found there and in their references, as well as in [11] and [18], for example. See also [17]. Examples of intensities arising i... |

10 |
Le Théorème d’Arrêt en une Fin d’Ensemble
- Azéma, Jeulin, et al.
- 1993
(Show Context)
Citation Context ... some sequence of t ↘ 0). Since L belongs to the predictable set {t : Bt = 0}, the compensator dAL is a.s. supported by this set, but this set has Lebesgue measure 0, so dAL is a.s. singular. In fact =-=[1, 27]-=-, a simple calculation shows that for t < 1, Zt = P (L > t|Ft) = 2Φ(−|Bt|/ √ 1 − t), where Φ is the standard normal distribution function, and dAL √ 2 t = π(1−t) dL0t , where L0 is the local time at 0... |

7 | Representation of Semimartingale Markov - Cinlar, Jacod - 1981 |

7 |
The Market Price of credit risk : the impact of Asymmetric Information
- Giesecke, Goldberg
- 2008
(Show Context)
Citation Context ...to Lévy systems was recently recalled in the work of X. Guo and Y. Zeng [12], and examples of intensities arising in the field of Credit Risk can be found there and in their references, as well as in =-=[11]-=- and [18], for example. See also [17]. Examples of intensities arising in the field of Survival Analysis can be found in the book of Fleming and Harrington [9]. Corollary 10 Let X = (Ω, X, P µ) be a s... |

6 |
Jumping Filtrations and Martingales with Finite Variation, Séminaire de Probabilités
- Jacod, Skorohod
- 1994
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Citation Context ...nce, by (13), dKt ≪ dt. In particular Kt is continuous and is thus a version of the additive functional H, so dHt ≪ dKt ≪ dt. A useful result related to Theorem 9 is the following. Jacod and Skorohod =-=[16]-=- define a jumping filtration F to be a filtration such that there exists a sequence of stopping times (Tn)n=0,1,... increasing to ∞ a.s. with T0 = 0 and such that for all n ∈ N, t > 0, the σ-fields Ft... |

4 |
Information reduction via level crossings in a credit risk model
- Jarrow, Protter, et al.
- 2007
(Show Context)
Citation Context ...ystems was recently recalled in the work of X. Guo and Y. Zeng [12], and examples of intensities arising in the field of Credit Risk can be found there and in their references, as well as in [11] and =-=[18]-=-, for example. See also [17]. Examples of intensities arising in the field of Survival Analysis can be found in the book of Fleming and Harrington [9]. Corollary 10 Let X = (Ω, X, P µ) be a semimartin... |

1 |
Rate for Credit Risk and Hedging Defaultable Claims, Finance and Stochastics
- Blanchet-Scaillet, Jeanblanc, et al.
(Show Context)
Citation Context ...) we have that d〈Z, M〉t ≪ d〈M, M〉t ≪ dt, a.s. The result follows. A topic that has achieved importance recently in the theory of Credit Risk is that of the Expansion of Filtrations. See, for example, =-=[2]-=-, [6], or [19]. In the case of initial expansions, we can expand using Jacod’s criterion (see [14] or [26, p. 371]) by adding a random variable L to the filtration F at time 0, provided that for each ... |

1 |
Progressive Enlargement of Filtrations with
- Jeanblanc, Cam
(Show Context)
Citation Context ...t d〈Z, M〉t ≪ d〈M, M〉t ≪ dt, a.s. The result follows. A topic that has achieved importance recently in the theory of Credit Risk is that of the Expansion of Filtrations. See, for example, [2], [6], or =-=[19]-=-. In the case of initial expansions, we can expand using Jacod’s criterion (see [14] or [26, p. 371]) by adding a random variable L to the filtration F at time 0, provided that for each t ≥ 0 the (reg... |

1 | Grossissements de Filtrations: Exemples et - Jeulin |