A Stochastic Approach to Modeling the Managerial Information Processing Dejun Xie * and Dung Nguyen † Abstract—This work concerns the stochastic mod- eling of business information received by a company from managerial’s point of view. A mean reverting stochastic process is proposed to model the percent of information that a company can receive at any time t. Explicit iterative formulas are provided under cer- atin assumptions. Numerical scheme is derived for computing the total effective information received for a given period. Keywords: managerial, information processing, stochas- tic modeling, mean-reverting process, numerical simula- tion 1 Introduction A company’s managerial function can be described as an information processing system, where the external world is treated as information generator and the management team of the company as information receiver. External information, in forms such as industry regulations, market competition, feedback from client, and credit ratings, creates a business climate in which that the company need to fit. The task of a manager is to process the received information and make sensible decisions in order to accomplish the executive goal. To respond to the external information in a timely manner is crucial for the company to survive the more than ever competitive market in the e-commerce era. Because of the important implications in real economy, there exist considerable studies devoted to such topics. Many of the previous studies are from the point of view of organizational learning, the semantic of which can be found in [7], for instance. Similar approaches are applied in [4, 5, 12], [9]. A more complete literature review relevant to organizational learning can be found in [6]. Here we are more interested in the stochastic modeling of information flow in itself and providing a rigorous mathematical model to calculate how much information a company may lose or receive in a given period of time and given number of qualified managers. Our study is built on the assumption that the pro- * Department of Mathematics, University of Delaware, Newark, DE 19716, USA. Email: dxie@math.udel.edu † Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA. Email: nguyen@pitt.edu cessing ability of any manager is not infinite. First, let us consider a very special case where the external world, as an information generator, generates N bits of information periodically at every T unit time. and the manager has an information processing capability of greater or equal to N/T , which means that the manager is able to process at least N bits of information in the time interval T . It is assumed that the information transmitting time from the external world to the man- ager is negligible. In this case, no information loss at the manager’s office would occur. Hence no deputy managers are needed. Here a deputy manager could mean a consultant, a secretary, or a vice manager. However, in real situations, the external informa- tion arrives at random rates and at random speed. It may arrive at the managerial office any time before or after office hours. Here we are interested in what percent of information a company may lose at any given number of business managers z and time t. We seek a method to compute what quantity of the total information that a company may receive or miss in a infinite period of time, given the function (could be stochastic) governing infor- mation growth. Introduce, say, q(z,t) be the percentage of information loss we are interested in. Intuitively q is decreasing in z for fixed t, since more managers will increase the capability of information processing. In the following sections, we first study a discrete case, where z is assumed to be non-negative integers. Under some assumptions, one can see explicit iteration formulas for computing information inefficiency can be obtained. Then we focus on the continuous case, and propose a stochastic differential equation for modeling the percent of information that a company can receive in a specified time duration. The analytical features of the process, including the approximated transitional density functions, are provided. An algorithm is derived for computing the singular integrations appeared in the model. We finished the paper by providing numerical simulations and implications. 2 Discrete Information Processing Let’s descretize the time interval [0,T 0 ] by a vector of points (t 1 ,t 2 ,t 3 , ..., t k , ...). Since the inflow of informa- tion is of stochastic nature in both time and quantity,