1. Introduction -- 2. Architecture of grey forecasting models -- 3. Mechanism and reduction of grey forecasting models -- 4. Continuous-time grey endogenous forecasting models -- 5. Discrete-time grey endogenous forecasting models -- 6. Continuous-time grey exogenous forecasting models -- 7....

In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim...

In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim...

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena.

"This book provides empirical research or studies on the formation of mathematical abilities in the context of the Fourth Industrial Revolution regarding its development of both teaching and learning strategies, as well as the use of ICT in the development of this student knowledge"--

Despite there are useful books and text books from recognized authors about modeling macroeconomics through various types of methods and methodologies, “Some Useful tips in Modeling a DSGE models” try to add special features through an economist can use to model macro and micro relations to...

Модель Харрода (Harrod) в дифференциальной форме на самом деле имеет дискретный характер, и вытекающий из нее рост экономики по экспоненте – иллюзорен. Ошибка...

Harrod method in the differential form has a discrete character and the resulting growth of economy exponentially is insubstantial. The mistake is based on adjunction of the capital and annual income through a constant ratio. This becomes clear from the positions of study of dimensionality of...

Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’...

Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’...

This paper constructs an assignment model that allocates a variable number of labor to a variable amount of capital. Sattinger introduced an assignment model in which a worker is coupled with a machine. In Sattinger's model, workers and machines differ in quality, e.g., ability, productivity,...

This book provides the first practical guide to the function and implementation of algorithmic differentiation in finance. Written in a highly accessible way, Algorithmic Differentiation Explained will take readers through all the major applications of AD in the derivatives setting with a focus...

A first order linear differential equation is used to describe the dynamics of an investment fund that promises more than it can deliver, also known as a Ponzi scheme. The model is based on a promised, unrealistic interest rate; on the actual, realized nominal interest rate; on the rate at which...

This paper deals with the assessment of options on dividend paying stock and futures options. We start from the case of the underlying asset who does not generate dividend and then switch to an underlying asset which pays a continuous dividend yield. The final conditions and the boundary...

The complex of mathematical models of investigated indicators has been developed to study the dynamics of budget indicators, forecasttheir change and plan revenues and expenditures of state and local budgets appropriately. This is a linear dynamic model withconstant and variable coefficients,...

In estimating the number of failures using right truncated grouped data, we often encounter cases that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease spread predictions, the SIR model described by simultaneous...

Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden...

Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden...

In this work we introduce a method, by using the least-squares method and a Schauder basis, which provides a numerical solution for a wide class of linear differential or integral equations. In addition, we give a convergence result and an application.

Functional classes of Lorenz curves are derived from a generalization of a relative poverty notion. All these Lorenz curves compare individual income to the average of all larger or all smaller incomes. The parameters of the Lorenz curves are effectively computed from empirical income data by...

In this paper we start from a continuous time framework derived from the classical predator-prey model in order to analyze the recent dynamics of regional evolution in the EU. The model describes a system of interrelated units obeying a complex functional dynamics that at any moment may...

Formulae are derived for the characteristic function of the inverted Dirichlet distribution and hence the multivariate F. The analysis involves a new function with multiple arguments that extends the confluent hypergeometric function of the second kind. This function and its properties are...

The integration of differential equations by recurrent power series is a classical method in ODE. This method is valid on very long spans of integration and unusually large step-sizes. However, this method is rarely used, mainly since each problem requires a specific formulation.