A Ciesielski-Taylor type identity for positive self-similar Markov processes

The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly a new transformation which maps a subset of the family of Laplace exponents of spectrally negative L\'evy processes into itself. Secondly some classical features of fluctuation theory for spectrally negative L\'evy processes as well as more recent fluctuation identities for positive self-similar Markov processes

Finite element modelling of sheathed cold-formed steel beam-columns

The structural behaviour of sheathed cold-formed steel lipped channel section columns (studs) subjected to combined compression and major axis bending is investigated herein by means of numerical modelling. Finite element (FE) models of single studs, set in tracks and connected to oriented strand board (OSB) and gypsum plasterboard sheathing under varying combinations of axial compression and horizontal loading were developed in ABAQUS and validated against experimental results reported in the literature. The developed numerical models incorporated cross-sectional and global geometric imperfections, while geometrical and material nonlinearities for both the steel and the sheathing were considered in the analyses. Particular emphasis was given to replicating the “as-built” boundary conditions at the ends of the columns, controlled by the screws connecting the column to the track and by the column–track contact interaction. The interaction between the sheathing and the column, as well as the behaviour of the fasteners connecting the two components, were also explicitly modelled. Both the shear and pull-through characteristics of the fasteners were considered and simulated based on experimental findings. Following successful validation of the finite element models, parametric studies were conducted. The results showed that substantial structural performance benefits can be achieved by the addition of sheathing to cold-formed steel members and that the spacing of the connectors has a strong influence on the member response. For a typical system, decreasing the connector spacing from 300 mm to 75 mm was found to increase stud capacity and stiffness by up to 12% and 10% respectively when in pure compression and up to 26% and 22% respectively when in pure bending; under combined loading, capacity increases of up to 29% were found

Energy poverty policies and measures in 5 EU countries: a comparative study

Energy Poverty (EP) is the inability to attain a socially and materially necessitated level of domestic energy services. In the EU this occurs primarily due to low incomes, poor energy performance of buildings and high energy costs. The impacts of EP range from impaired social lives to unhealthy living conditions, with further consequences in the physical and mental health of energy poor individuals. Member states have been assigned by the EU with the responsibility of dealing with EP within their own territories. This is attainable mainly by creating effective policies, while also encouraging synergies among policies of different fields. However, scientific knowledge is gathered and action is taken on a national level only in a limited number of EU countries. For this reason, this paper aims to fill in the gap and capture snapshots from five EU countries (Cyprus, Spain, Portugal, Bulgaria and Lithuania) where EP has not been exhaustively examined. The study provides an overview of selected policies and measures directly or indirectly targeting EP alleviation and analyses their history and evolution at an EU level as well as at national level. It considers the different geographical dimensions, conditions and aspects (e.g. national or regional) where EP is encountered, in an attempt to identify any variances or similarities in the approaches adopted. Through this comparative study, strengths and weaknesses of national strategies are identified and analysed. Conclusively, based on this analysis, recommendations are made on how to utilise policy tools and provide the most efficient support to energy poor households in the corresponding countries

Large deviations for clocks of self-similar processes

The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a L\'evy process drifting to $\infty$ and its inverse, the clock of the corresponding positive self-similar process. We describe here asymptotical properties of these clocks in large time, extending the results of Yor and Zani

On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. Kyprianou, Loeffen and Perez [28] have shown that a refraction strategy (also called threshold strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. In this paper, we propose an alternative approach to this optimal problem.Comment: 16 page

Superprocesses as models for information dissemination in the Future Internet

Future Internet will be composed by a tremendous number of potentially interconnected people and devices, offering a variety of services, applications and communication opportunities. In particular, short-range wireless communications, which are available on almost all portable devices, will enable the formation of the largest cloud of interconnected, smart computing devices mankind has ever dreamed about: the Proximate Internet. In this paper, we consider superprocesses, more specifically super Brownian motion, as a suitable mathematical model to analyse a basic problem of information dissemination arising in the context of Proximate Internet. The proposed model provides a promising analytical framework to both study theoretical properties related to the information dissemination process and to devise efficient and reliable simulation schemes for very large systems

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl

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