On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations

We investigate joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient α ∈ (0, 1) and with idiosyncratic Poisson innovations. Assuming that α has a density function of the form ψ(x) (1 − x) β , x ∈ (0, 1), with β ∈ (−1, ∞) and lim x ↑ 1 ψ ( x ) = ψ 1 ∈ ( 0 , ∞ ) $\lim\limits_{x\uparrow 1} \psi(x) = \psi_1 \in (0, \infty)$ , different limits of appropriately centered and scaled aggregated partial sums are shown to exist for β ∈ (−1, 0] in the so-called simultaneous case, i.e., when both N and the time scale n increase to infinity at a given rate. The case β ∈ (0, ∞) remains open. We also give a new explicit formula for the joint characteristic functions of finite dimensional distributions of the appropriately centered aggregated process in question.

A closed-form pricing formula for catastrophe equity options

In this article, we derive a closed-form pricing formula for catastrophe equity put options under a stochastic interest rate framework. A distinguishing feature of the proposed solution is its simplified form in contrast to several recently published formulae that require evaluating several layers of infinite sums of $n$ -fold convoluted distribution functions. As an application of the proposed formula, we consider two different frameworks and obtain the closed-form formula for the joint characteristic function of the asset price and the losses, which is the only required ingredient in our pricing formula. The prices obtained by the newly derived formula are compared with those obtained using Monte-Carlo simulations to show the accuracy of our formula.

Preliminary Design for Segmental Joint of Precast Tunnel Liner

Responses of the segmental tunnel liner to external forces are primarily dependent on complicated interactions among construction process, soil structural interactions, segmental (longitudinal) joint characteristic etc. However, most proposed liner’s design procedures and recommendations are basically empirical and experience based, especially when the roles of tunnel joint are concerned. In the present study, a preliminary design calculation for the segmental joint with consideration of three practical conditions was proposed. The method adopts two main assumptions; the stiffness reduction factor and simplified pre-stressed concrete blocks, so that the flexural capacity of the segmental joint and its interactions to the main reinforced concrete segment body can be designated. Calculation examples are given for three most probable cases, namely, 1) the unbolted joint without joint opening, 2) the bolted joint without joint opening and 3) the unbolted segmental joint with allowing joint opening. Based on these calculations, the required compressive strength of concrete, thickness of liner, steel reinforcement, bolts and number of segments of the liner could be specified. The proposed method could well provide an engineer a tool to determine the initial joint configuration and its interaction to the overall tunnel lining.

Efficiency and Stiffness of the Single Lap Bolt Joints in Glass Epoxy Composites

The present work deals with the investigations on the joint efficiency and the joint stiffness of the single lap bolt joint made of two dimensional woven glass fibre reinforced composite materials. The effect of joint geometry, bolt pretension and washer has been determined on the bolt joint performance. To estimate the effect of geometric parameters; the edge-to-hole diameter (e/d) and width-to-hole diameter (w/d) ratios are varied from 3 to 4 and 3 to 5, respectively. To study the worst loading conditions; the bolt pre-tension is set to zero, whereas 5 Nm torque is applied to investigate the joint in fully clamped conditions. Two different sizes of washer i.e., the outer diameter of 12 mm and 16 mm have been studied to estimate the effect of the washer on failure load, joint stiffness, and joint efficiency. Progressive damage analysis has been performed on the single lap bolt joint. Characteristic curve method along with Tsai-Wu failure criteria has been used for the prediction of the failure loads and failure modes. The joint stiffness and the failure load of the joint are increased with the increase of w/d ratios. However, the joint efficiency was negatively influenced by w/d ratio.

Adhesive Joint Model for Delamination Analysis of a Co-Cured Composite Joint: Applicability and Limitation

Modeling the interface between two adherents in a co-cured composite joint for a delamination analysis is always a challenge since properties and thickness of the material forming the interface are not clearly defined or well characterized. In a conventional finite element (FE) analysis using virtual crack closure technique (VCCT) based on a linear elastic fracture mechanics (LEFM) theory, adherents are assigned to share the same common nodes along their intact interface. On the other hand, an FE analysis using cohesive elements or analytical methods based on an adhesive joint model for a delamination analysis of a co-cured joint will require modeling of the interface as well as the appropriate selection of its thickness and properties. The purpose of this paper is to establish the applicability and limitation of the adhesive joint model for a delamination analysis of a co-cured composite joint. In particular, it will show that when certain requirements are met, the strain energy release rates (SERR) become independent or nearly independent of the adhesive stiffness and thickness, and thus, SERR of an adhesive joint will be the same as that for a co-cured joint. These requirements are determined from a theoretical consideration, and they can be expressed explicitly in terms of joint characteristic (or load transfer) lengths and joint physical lengths. The established requirements are further validated by numerical results for various cracked joint geometries. Finally, implication of a mode ratio obtained by the proposed adhesive joint model for a corresponding delamination crack is discussed.

Measures for concordance and discordance with applications in disease control and prevention

Bivariate binary response data appear in many applications. Interest goes most often to a parameterization of the joint probabilities in terms of the marginal success probabilities in combination with a measure for association, most often being the odds ratio. Using, for example, the bivariate Dale model, these parameters can be modelled as function of covariates. But the odds ratio and other measures for association are not always measuring the (joint) characteristic of interest. Agreement, concordance, and synchrony are in general facets of the joint distribution distinct from association, and the odds ratio as in the bivariate Dale model can be replaced by such an alternative measure. Here, we focus on the so-called conditional synchrony measure. But, as indicated by several authors, such a switch of parameter might lead to a parameterization that does not always lead to a permissible joint bivariate distribution. In this contribution, we propose a new parameterization in which the marginal success probabilities are replaced by other conditional probabilities as well. The new parameters, one homogeneity parameter and two synchrony/discordance parameters, guarantee that the joint distribution is always permissible. Moreover, having a very natural interpretation, they are of interest on their own. The applicability and interpretation of the new parameterization is shown for three interesting settings: quantifying HIV serodiscordance among couples in Mozambique, concordance in the infection status of two related viruses, and the diagnostic performance of an index test in the field of major depression disorders.

Joint Characteristic Effect on the Performance of Nonlinear Piezoelectric Energy Harvesters

In this work, the effects of joint characteristics on the performance of a nonlinear piezoelectric energy harvester are investigated numerically. Large amplitude deflection unimorph beam with a tip mass and a nonlinear piezoelectric layer is considered as an energy harvester. By applying Euler-Lagrange equation and the Gauss’s law, mechanical and electrical equations of motion are obtained respectively, under two scenarios, i.e. with an ideal (rigid) joint and with a flexible one. A numerical approach is followed to investigate the effects of each nonlinear parameter of the harvester (stiffness, damping and piezoelectric coefficient) on harvested power. Results show that considering ideal joint between harvester and base structure leads to overestimating the maximum output power and the range of effective excitation frequency.

BOUNDS ON PRICES FOR ASIAN OPTIONS VIA FOURIER METHODS

The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.