Approximating distributional behaviour of LTI differential systems using Gaussian function and its derivatives

The paper is concerned with defining families of smooth functions that can be used for the approximation of impulsive types of solutions for linear systems. We review the different types of approximations of distributions in terms of smooth functions and explains their significance in the characterization of system properties where impulses were used for their characterisation. For controllable systems, we establish an interesting relation between the time t and sigma (volatility) in the approximation of distributional solutions. An algorithm is then proposed for the calculation of the coefficients of the input required to minimize the distance of our desired target state before and after approximation is proposed. The optimal choice of sigma is derived for a pre-determined time t for the state transition

Effects of loss aversion on neural responses to loss outcomes: an event-related potential study

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Loss aversion is the tendency to prefer avoiding losses over acquiring gains of the same amount. To shed light onthe spatio-temporal processes underlying loss aversion, we analysed the associations between individual lossaversion and electrophysiological responses to loss and gain outcomes in a monetary gamble task.Electroencephalographic feedback-related negativity (FRN) was computed in 29 healthy participants as thedifference in electrical potentials between losses and gains. Loss aversion was evaluated using non-linearparametric fitting of choices in a separate gamble task.Loss aversion correlated positively with FRN amplitude (233–263 ms) at electrodes covering the lower face.Feedback related potentials were modelled by five equivalent source dipoles. From these dipoles, strongeractivity in a source located in the orbitofrontal cortex was associated with loss aversion.The results suggest that loss aversion implemented during risky decision making is related to a valuationprocess in the orbitofrontal cortex, which manifests during learning choice outcomes

An investigation of the theory of bank portfolio allocation within a discrete stochastic framework using optimal control techniques

In this paper, it is fully developed a control model considering the evolution of value of bank's Assets. The basic difference equation of the system is designed, including six control variables (three of them determining the mix of investments for bonds, loans and cash, the extra rate of return to customers due to deposits, the rate of capital represents the amount of net equity issuing (i.e. dividends) and the banking cost) and fulfilling a smoothness criterion described by a quadratic functional. The state variable of the system corresponds to the value of bank's Assets can oscillates deliberately absorbing fluctuations in the different parameters involved. The theoretical model is solved using standard linearization and advanced stochastic optimization techniques resulting analytic formulae for the six control variables. These solutions are actually feedback mechanisms of the past value of bank's Assets. At the end, a practical application for the banking system is presented deriving a smooth solution for the development of the six controllers. © Taru Publications

On linear generalized neutral differential delay systems

In this paper, the class of linear generalized neutral differential delay systems with time-invariant coefficients is studied. These kinds of systems are inherent in many physical and engineering phenomena. Using the matrix pencil theory, we decompose it into five subsystems, whose solutions are obtained. Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable. © 2009 The Franklin Institute

Linear generalized stochastic systems for insurance portfolios

We consider a typical portfolio of different insurance products and investigate the pricing process using the framework of a linear time invariant generalized stochastic discrete-time model. Moreover, we assume that, due to regulatory constraints, the resulting system is (regular) descriptor and calculate the solution using the tools of matrix pencil theory. Finally, we present a numerical application for two different portfolios. © Taylor & Francis Group, LLC

On generalized regular stochastic differential delay systems with time invariant coefficients

In this article, we consider the generalized linear regular stochastic differential delay system with constant coefficients and two simultaneous external differentiable and non differentiable perturbations. These kinds of systems are inherent in many application fields; among them we mention fluid dynamics, the modeling of multi body mechanisms, finance and the problem of protein folding. Using the regular Matrix Pencil theory, we decompose it into two subsystems, whose solutions are obtained as generalized processes (in the sense of distributions). Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable. Finally, two illustrative applications are presented using white noise and fractional white noise, respectively

Generalized inverses of the vandermonde matrix: Applications in control theory

In the literature of control and system theory, several explicit formulae appeared for solving square Vandermonde systems and computing the inverse of it. In the present paper, we will discuss and present analytically the generalized inverses of the rectangular and square Vandermonde matrix. These matrices have been appeared recently in an interesting control and system theory problem, where the change of the initial state of a linear descriptor system in (almost) zero time is required. © 2013 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg

On the solution of higher order linear homogeneous complex σ-α Descriptor matrix differential systems of Apostol-Kolodner type

In this paper, the solution of higher order linear homogeneous complex σ-α descriptor matrix differential systems of Apostol-Kolodner type is investigated by considering pairs of complex matrices with symmetric and skew symmetric structural properties. The results are very general, and they derive under congruence of the Thompson canonical form. The regularity (or singularity) of a matrix pencil pre-determines the number of sub-systems respectively. The special structure of these kinds of systems derives from applications in engineering, physical sciences and economics. A numerical example illustrates the main findings of the paper. © 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

Modeling Frost Losses: Application to Pricing Frost Insurance

The main objective of this article is to model the losses caused by frost events and use it to price frost insurance. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damage. The main challenges in modeling frost loss variables are, first, the nonlinearity of the frost losses with respect to the temperature and, second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurance for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk, and Wang's premium based on temperature data from San Joaquin Drainage in California. Copyright © 2018 Society of Actuaries