Paper Title
A Stochastic Economic Model Using Modified Nonhomogeneous Poisson Process with a Birth and Death Diffusion Intensity Rate and External Jump Processes

Abstract
One of the important functions of the economists is to provide information on the future trend of economic developments, which is important to plan for human activities. Today, economists are interested in describing phenomena in theoretical models involving economic structure by considering the stochastic analogs of classical differences and differential equations. In this paper a description of a stochastic economic model using a modified nonhomogeneous Poisson process is considered. More specifically, the nonhomogeneous Poisson process is derived using an intensity rate follow a birth and death diffusion process with random external jump process. The mean and the variance approximation as well as the predicted and the simulated sample path of such a stochastic economic process are also obtained. Numerical examples for the case of no jumps as well as the case of the occurrence of jump process that follow a uniform and exponential distributions are considered. Keywords - Stochastic Economic Model, Birth-Death Diffusion Process, External Jump Process, Intensity Rate Process, Nonhomogeneous Poisson Process.