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Martingale representations in progressive enlargement by multivariate point processes
No full textIn this paper, we show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete marks space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal
Martingale representations in progressive enlargement by the reference filtration of a semi-martingale: a note on the multidimensional case
No full textLet X and Y be an m-dimensional F-semi-martingale and an n-dimensional H-semi-martingale, respectively, on the same probability space (Omega, F, P), both enjoying the predictable representation property. We propose two representation results for the square-integrable G-martingales, where G = F boolean OR H. As a first application, we identify the biggest possible value of the multiplicity in the sense of Davis and Varaiya of Vi-1(d) F-i where, fixed i is an element of (1, ..., d), F-i is the reference filtration of a martingale M-i, which enjoys the (P, F-i)-predictable representation property. This result helps us to identify a basis of martingales for the Poisson filtration enlarged by a general random time. A second application falls into the framework of credit risk modelling and in particular into the study of progressive enlargement of the market filtration by a default time. We present a new proof of the analogous of classical Kusuoka's theorem, when the risky asset price is a multidimensional semi-martingale enjoying the predictable representation property and the default time satisfies the density hypothesis
Symmetric models for lifetimes: the role of exchangeable equivalence relations
No full textA model of a heterogeneous population partitioned into a finite number of classes according an exchangeable equivalence relation is studied, With this motivation the properties of exchangeable equivalence relations are investigated and, in particular, the structure of its equivalence classes is characterized
An example of martingale representation in progressive enlargement by an accessible random time
No full textExchangeable mixture models for lifetimes: the role of "occupation numbers
No full textWe study several aspects of a special type of exchangeable distributions. These distributions arise when considering the lifetimes of the individuals in a population divided into d different subpopulations and there is a (symmetric) dependence among categories of single individuals. The role of “occupation numbers” in this context is highlighted
Filtering equations for the conditional law of residual lifetimes from a heterogeneous population
No full textWe consider a probabilistic model of a heterogeneous population subdivided into homogeneous sub-populations. A main assumption is that the "frailties" give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals
Continuous time random walks and queues: Explicit forms and approximations of the conditional law with respect to local times
No full textIn the filtering problem considered here, the state process is a continuous time random walk and the observation process is an increasing process depending deterministically on the trajectory of the state process. An explicit construction of the filter is given. This construction is then applied to a suitable approximation of a Brownian motion and to a rescaled MIM/I queueing model. In both these cases, the sequence of the observation processes converges to a local time, and a convergence result for the respective filters is given. The case of a queueing model when the observation is the idle time is also considered. (C) 2006 Elsevier B.V. All rights reserved
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Exchangeable mixture models for lifetimes: the role of "occupation numbers''.
No full textWe study several aspects of a special type of exchangeable distributions. These distributions arise when considering the lifetimes of the individuals in a population divided into d different subpopulations and there is a (symmetric) dependence among categories of single individuals. The role of “occupation numbers” in this context is highlighted
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