Stock loan with Automatic termination clause, cap and margin

This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared to stock loans without any constraints. The automatic termination clause, cap and margin are in fact a stop order set by the bank. Mathematically, it is a kind of optimal stopping problems arising from the pricing of financial products which is first revealed. We aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters : this loan size, interest rate, cap, margin and fee for providing such a service and quantity of this automatic termination clause and relationships among these parameters as well as the optimal exercise times. We present numerical results and make analysis about the model parameters and how they impact on value of stock loan.Comment: 30 pages, 7 figure

An Examination of the Editors and Friendship of the Tang Songs and Poems in the Classification of the Categories

Zhao Mengkui’s compilation of Tang poems is one of the largest collections of Tang poems in the Southern Song Dynasty, and has served as a guide in the history of the compilation of Chinese Tang poems. Zhao Mengkui, the compiler of the “Tang Songs and Poems”, was born into a royal family of imperial examiners and had excellent family roots and profound academic training. The problem of the different records of Zhao Mengkui’s origin is due to the fact that he lived in a different place of official transfer. In his life, Zhao Mengkui had a close personal friendship with Liu Kezhuang, Li Qianwei, Lin Xiyi, and other literati. It is an important reference value for the study of the compilation of the Tang Songs and Poems

Fast Optimal Joint Tracking-Registration for Multi-Sensor Systems

Sensor fusion of multiple sources plays an important role in vehicular systems to achieve refined target position and velocity estimates. In this article, we address the general registration problem, which is a key module for a fusion system to accurately correct systematic errors of sensors. A fast maximum a posteriori (FMAP) algorithm for joint registration-tracking (JRT) is presented. The algorithm uses a recursive two-step optimization that involves orthogonal factorization to ensure numerically stability. Statistical efficiency analysis based on Cram\`{e}r-Rao lower bound theory is presented to show asymptotical optimality of FMAP. Also, Givens rotation is used to derive a fast implementation with complexity O(n) with $n$ the number of tracked targets. Simulations and experiments are presented to demonstrate the promise and effectiveness of FMAP

Computational nonlinear vibration analysis for distributed geometrical nonlinearities in structural dynamics

The demand to reduce the impact of aviation on the environment is leading jet engine manu- facturers to increase the fuel and propulsion efficiency of the engines. This in turn is pushing materials to their physical limits by undergoing increasingly higher thermo-mechanical loads. In this regime, blades and other engine components are subjected to large deforma- tions generating nonlinearities that activate new failure mechanisms not dealt with before. Therefore, vibration analysis is essential to develop new methodologies for the accurate prediction of components’ behaviour. This research focuses on investigating the effect of the distributed geometric nonlinearities and rotational speed on the dynamic behaviour of three-dimensional structures. The Green-Lagrange strain measures are employed in this research to express the nonlinear relationship between the displacement and the strain. The nonlinear algorithms used for the numerical simulations are developed based on the Finite Element Method combined with the Harmonic Balance method. The complex geometries are discretised by using the geometric exact three-dimensional solid elements. The forced response functions and the backbone curves for the steady-state response of the nonlinear system can be computed. The research aims to develop and validate methodologies for the identification and control of undesired vibration modes which will inform new design choices. Finite element modelling of the blades generally involves an immense number of degree-of-freedoms, which could be infeasible to compute. The reduced order modelling (ROM) techniques are crucial for achieving an accurate prediction of the nonlinear behaviour in an efficient way. Detailed computation strategies for the intrusive ROM methods are delivered. ROM techniques based on the linear and nonlinear mapping between the full model and the reduced basis are presented. The capabilities and limitations of both methods are assessed. The projection method based on the linear eigenmodes only has a slow converge to the full system. On the other hand, the quadratic manifold method with the static modal derivatives involved in the reduced coordinates provides a fast convergence.Open Acces

Intermetalic Growth Rate in Transient Liquid Phase Sintering of Pb-Free Solder Interconnects

Following the electron devices are widely used in daily life, Pb-free solder alloy, as the replacement of Pb solder joint material, needs extensive researches to observe the properties for using and simulation purpose. Solder are used as the joint to connect two work pieces in printed wiring board of electronics. Most lead-free solders comprise tin (Sn) as the majority component, and nominally pure b-Sn is the majority phase in the microstructure of these solders. The most important thing for solder joint that researchers care about is its life cycle. Due to the incomplete of the mechanical profile of Pb-free solder joint for now, this research worked on obtain data of life cycles. At the boundary of the Sn phase and Ag phase, the intermetallic would grow during the heating process, which affects the life cycle of the solder. This study incorporates mechanical testing and measurement of the intermetallic in scanning electron microscope (SEM) images in image J, to get enough data of life cycle to form a profile and the effects of the intermetallic. The measurement on images shows that the intermetalic layer grows in scallop-shape and the thickness increases with the temperature and sintering time. The growth rate can be modeled as a linear equation of the power of one half of the sintering time. This measurement will contribute to the ongoing research about the transit liquid phase sintering and the ball-grid array (BGA) reliability