Proceedings of ISER - Sciencefora International Conference, Kuala Lumpur, Malaysia, 1 st -3 rd October, 2019 3 A STOCHASTIC ECONOMIC MODEL USING MODIFIED NONHOMOGENEOUS POISSON PROCESS WITH A BIRTH AND DEATH DIFFUSION INTENSITY RATE AND EXTERNAL JUMP PROCESSES BASEL M. AL-EIDEH Kuwait University, College of Business Administration, QMIS Department, Kuwait E-mail: basel@cba.edu.kw 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. I. INTRODUCTION Poisson Processes either homogeneous or Nonhomogeneous play an important and a fundamental rule in theory and applications that embrace queuing and inventory models, population growth, engineering systems, maintenance theory, economic development, etc. This paper shows how decision makers’ concerns about model specification can affect the trend of economic developments. The importance of using this new approach of stochastic economic process using a modified nonhomogeneous Poisson process in economic models because this model is from the type of continuous – time models which is different from what we have already known from the discrete-type models and this kind of models is not widely used in various economic models. David (1997) studies a model in which production is linear in the capital stocks with technology stocks that have hidden growth rates. Veronesi (1999) studies a permanent income model with a riskless linear technology. Dividends are modeled as an additional consumption endow cent. Hidden information was introduced into asset pricing models by Detemple (1986), who considers a production economy with Gaussian unobserved variables. Al-Eideh and Hasan (2002) have considered growth price models under random environment using a solution of stochastic differential equation of the logistic price model as well as the logistic price models with random external jump process. They derived the steady state probability and the time dependent probability functions. Also, the mean and the variance as well as the sample path of such a process are considered. During this past decade there has been increasing effort to describe various facts of dynamic economic interactions with the help of stochastic differential processes. Thus stochastic differential processes provide a mechanism to incorporate the influences associated with randomness, uncertainties, and risk factors operating with respect to various economic units (stock prices, labor force, technology variables, etc.) Therefore, the techniques of stochastic processes become relevant in pursuing quantitative studies in economics. Stochastic modeling techniques are not only enable us to obtain reliable estimates of certain useful economical parameters but also provides indispensable tools for estimating parameters which are often associated with a high degree of non- sampling errors. Thus, it is proposed to introduce a study of economic structure using the techniques of stochastic processes. More specifically, the theory and applications of the Nonhomogeneous Poisson process have been studied from different points of view by Mukherjee et al. (1964), Boswell (1966), Basawa and Brockwell (1978), Basawa and Rao (1980), Grandel (1976), Keiding (1974), MacLean (1974), Hoel et al. (1972), Gusak (1998), (1999), Taylor and Karlin (1984). In particular Mukherjee et al. (1964), He used a generalized form of Poisson process for explanation of economic development with applications to India data. Also, Gusak (1999) studied the Ruin problems for Nonhomogeneous semi continuous integer-valued process. Numerous researchers have worked on studying various economic units from different points