A L\'evy input fluid queue with input and workload regulation

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment $i$ of the L\'evy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of L\'evy processes, to workload and queuing models

American Step-Up and Step-Down Default Swaps under Levy Models

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Levy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Levy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.Comment: 35 pages, 5 figure

Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a "message", then under the transformed measure the original Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy process, which we call the fiducial process, represents the "noise type". Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

High level expression of differentially localized BAG-1 isoforms in some oestrogen receptor-positive human breast cancers

Sensitivity to oestrogens and apoptosis are critical determinants of the development and progression of breast cancer and reflect closely linked pathways in breast epithelial cells. For example, induction of BCL-2 oncoprotein expression by oestrogen contributes to suppression of apoptosis and BCL-2 and oestrogen receptor (ER) are frequently co-expressed in tumours. BAG-1/HAP is a multifunctional protein which complexes with BCL-2 and steroid hormone receptors (including the ER), and can suppress apoptosis and influence steroid hormone-dependent transcription. Therefore, analysis of expression of BAG-1 in human breast cancer is of considerable interest. BAG-1 was readily detected by immunostaining in normal breast epithelial cells and most ER-positive tumours, but was undetectable or weakly expressed in ER-negative tumours. BAG-1 positive cells showed a predominantly cytoplasmic or cytoplasmic plus nuclear distribution of staining. A correlation between ER and BAG-1 was also evident in breast cancer derived cell lines, as all lines examined with functional ER expression also expressed high levels of BAG-1. In addition to the prototypical 36 kDa BAG-1 isoform, breast cancer cells expressed higher molecular weight isoforms and, in contrast to BCL-2, BAG-1 expression was independent of oestrogens. BAG-1 isoforms were differentially localized to the nucleus or cytoplasm and this was also independent of oestrogens. These results demonstrate a close association between BAG-1 and functional ER expression and suggest BAG-1 may be useful as a therapeutic target or prognostic marker in breast cancer. © 1999 Cancer Research Campaig

The prolific backbone for supercritical superprocesses

We develop an idea of Evans and O'Connell (1994) [13], Englnder and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called 'backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical (1+β)-superprocesses given in Etheridge and Williams (2003) [11]. Our approach relies heavily on the use of DynkinKuznetsov N-measures. © 2011 Published by Elsevier B.V. All rights reserved