Thin times and random times' decomposition

The paper studies thin times which are random times whose graph is contained in a countable union of the graphs of stopping times with respect to a reference filtration $\mathbb F$. We show that a generic random time can be decomposed into thin and thick parts, where the second is a random time avoiding all $\mathbb F$-stopping times. Then, for a given random time $\tau$, we introduce ${\mathbb F}^\tau$, the smallest right-continuous filtration containing $\mathbb F$ and making $\tau$ a stopping time, and we show that, for a thin time $\tau$, each $\mathbb F$-martingale is an ${\mathbb F}^\tau$-semimartingale, i.e., the hypothesis $({\mathcal H}^\prime)$ for $(\mathbb F, {\mathbb F}^\tau)$ holds. We present applications to honest times, which can be seen as last passage times, showing classes of filtrations which can only support thin honest times, or can accommodate thick honest times as well

Non-Arbitrage Under Additional Information for Thin Semimartingale Models

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continuous (do not jump on predictable stopping times). Herein, we focus on the NUPBR for semimartingales models that live on thin predictable sets only and the progressive enlargement with a random time. For this flow of information, we explain how far the NUPBR property is affected when one stops the model by an arbitrary random time or when one incorporates fully an honest time into the model. This also generalizes \cite{choulli/deng} to the case when the jump times are not ordered in anyway. Furthermore, for the current context, we show how to construct explicitly local martingale deflator under the bigger filtration from those of the smaller filtration.Comment: This paper develops the part of thin and single jump processes mentioned in our earlier version: "Non-arbitrage up to random horizon and after honest times for semimartingale models", Available at: arXiv:1310.1142v1. arXiv admin note: text overlap with arXiv:1404.041

Hubbard Hamiltonian in the dimer representation. Large U limit

We formulate the Hubbard model for the simple cubic lattice in the representation of interacting dimers applying the exact solution of the dimer problem. By eliminating from the considerations unoccupied dimer energy levels in the large U limit (it is the only assumption) we analytically derive the Hubbard Hamiltonian for the dimer (analogous to the well-known t-J model), as well as, the Hubbard Hamiltonian for the crystal as a whole by means of the projection technique. Using this approach we can better visualize the complexity of the model, so deeply hidden in its original form. The resulting Hamiltonian is a mixture of many multiple ferromagnetic, antiferromagnetic and more exotic interactions competing one with another. The interplay between different competitive interactions has a decisive influence on the resulting thermodynamic properties of the model, depending on temperature, model parameters and assumed average number of electrons per lattice site. A simplified form of the derived Hamiltonian can be obtained using additionally Taylor expansion with respect to $x=\frac{t}{U}$ (t-hopping integral between nearest neighbours, U-Coulomb repulsion). As an example, we present the expansion including all terms proportional to t and to $\frac{t^2}U$ and we reproduce the exact form of the Hubbard Hamiltonian in the limit $U\to \infty$. The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another types of model Hamiltonians.Comment: 26 pages, 1 figure, LaTeX; added reference

Arbitrages in a Progressive Enlargement Setting

This paper completes the analysis of Choulli et al. Non-Arbitrage up to Random Horizons and after Honest Times for Semimartingale Models and contains two principal contributions. The first contribution consists in providing and analysing many practical examples of market models that admit classical arbitrages while they preserve the No Unbounded Profit with Bounded Risk (NUPBR hereafter) under random horizon and when an honest time is incorporated for particular cases of models. For these markets, we calculate explicitly the arbitrage opportunities. The second contribution lies in providing simple proofs for the stability of the No Unbounded Profit with Bounded Risk under random horizon and after honest time satisfying additional important condition for particular cases of models

Paediatric and adult bronchiectasis: Specific management with coexisting asthma, COPD, rheumatological disease and inflammatory bowel disease

Bronchiectasis, conventionally defined as irreversible dilatation of the bronchial tree, is generally suspected on a clinical basis and confirmed by means of chest high-resolution computed tomography. Clinical manifestations, including chronic productive cough and endobronchial suppuration with persistent chest infection and inflammation, may deeply affect quality of life, both in children/adolescents and adults. Despite many cases being idiopathic or post-infectious, a number of specific aetiologies have been traditionally associated with bronchiectasis, such as cystic fibrosis (CF), primary ciliary dyskinesia or immunodeficiencies. Nevertheless, bronchiectasis may also develop in patients with bronchial asthma; chronic obstructive pulmonary disease; and, less commonly, rheumatological disorders and inflammatory bowel diseases. Available literature on the development of bronchiectasis in these conditions and on its management is limited, particularly in children. However, bronchiectasis may complicate the clinical course of the underlying condition at any age, and appropriate management requires an integration of multiple skills in a team of complementary experts to provide the most appropriate care to affected children and adolescents. The present review aims at summarizing the current knowledge and available evidence on the management of bronchiectasis in the other conditions mentioned and focuses on the new therapeutic strategies that are emerging as promising tools for improving patients' quality of life

Projections, Pseudo-Stopping Times and the Immersion Property

Given two filtrations $\mathbb F \subset \mathbb G$, we study under which conditions the $\mathbb F$-optional projection and the $\mathbb F$-dual optional projection coincide for the class of $\mathbb G$-optional processes with integrable variation. It turns out that this property is equivalent to the immersion property for $\mathbb F$ and $\mathbb G$, that is every $\mathbb F$-local martingale is a $\mathbb G$-local martingale, which, equivalently, may be characterised using the class of $\mathbb F$-pseudo-stopping times. We also show that every $\mathbb G$-stopping time can be decomposed into the minimum of two barrier hitting times