Lahore School of Economics

The First Annual Conference on Mathematical and Statistical Models in Economics, Finance and Applied Sciences started on Friday February 6, 2015 at the Main Campus of Lahore School of Economics. 

The conference provided an opportunity for eminent Mathematicians, Physicists, Statisticians, Economists and Social Scientists from all over the country to come together and learn from each other. The conference was inaugurated by Dr. Shahid Amjad Chaudhry, Rector of the Lahore School of Economics and Dr. Rana Abdul Wajid, Director, Centre of Mathematics and Statistical Sciences, Lahore School of Economics who warmly welcomed all the guests and faculty members from institutions across the country. Dr. Shahid Amjad Chaudhry explained the critical objective of providing a platform for all likeminded academics from all over Pakistan to join together in research collaborations while Dr. Azam Chaudhry, Dean of Faculty of Economics, Lahore School of Economics delivered the keynote address on “The Role of Mathematics and Statistical Sciences in Social Sciences”.

The topic of the first session was Differential equations and Optimal control Techniques, which included talks by Dr. Adnan Khan and Dr. Amer Rasheed from Lahore University of Management Sciences, Dr. Rehana Naz from Lahore School of Economics. This session was chaired by Dr. Imran Naeem, Chairman of Department of Mathematics, Syed Babar Ali School of Sciences & Engineering, Lahore University of Management Sciences.

The second session was chaired by Dr. Mujahid Abass, Lahore University of Management Sciences. The topic of this session was Fuzzy Logics and Decision Making and it included speakers Dr. Ismat Beg and Dr. Asma Khalid Lahore School of Economics and Tabasam Rashid of National University of Computer and Emerging Sciences.

The third session was chaired by Dr. Theresa Chaudhry, Lahore School of Economics and the topic of the session was ‘Factors Affecting Economic Development and Growth’ and the speakers included Dr. Samina Naveed, Dr. Verda Salman and Zahid Siddique from the National University of Science and Technology.

Optimal Control Techniques in Epidemiology: How We Won the Fight against the Zombies

Adnan Khan, Department of Mathematics, Syed Babar Ali School of Sciences and Engineering, Lahore University of Management Sciences, Lahore


We consider time dependent control strategies for ODE based models for transmission dynamics of epidemics. We will describe the formulation of the general problem using Pontryagin’s maximum principle. To motivate the study we will give simple examples from economics and also look at a variant of the Zombie outbreak model of Smith et.al.

The Closed Form Solutions of Two Celebrated Economic Growth Models via Partial Hamiltonian Approach

Rehana Naz, Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore


This paper studies two celebrated Economic growth models: One sector Ramsey model with variable time preferences and two sector model of endogenous growth Lucas-Uzawa model. The closed form solutions play a vital role in economic dynamics to assess transition dynamics of endogenous economic growth models. The partial Hamiltonian approach is utilized to construct the closed form solutions to study dynamics of these models. This approach does not require the linearization process and the reduction of dimension technique usually adopted in literature. This study shows that for the Ramsey model, the growth rate of consumption and capital decrease over time as the steady state is approached whereas the gross saving rate remains constant. For the Lucas-Uzawa model, the growth rates of physical capital, consumption and human capital are constructed to study several features associated with transitional dynamics of this model.

Realistic simulations of dendritic solidification using Phase Field Method

Amer Rasheed, Department of Mathematics, Syed Babar Ali School of Sciences and Engineering, Lahore University of Management Sciences, Lahore

The understanding and control over the evolution of dendrites during the solidification process of metals and alloys has a critical impact on the final solidified material. In order to ameliorate the quality and properties of metals or alloys, the major industrial challenges lie in the possibility to control the metal structure and its blemishes (that occur during the solidification process). It has been observed experimentally that hydrodynamic motions in liquid phase have a considerable influence on structure and growth of dendrites. Moreover, it has been shown that the velocity and direction of fluid flow can be controlled by applying magnetic field. In order to analyze the dynamic behavior of dendrites under the action of magnetic field, we have developed an improved phase-field model which consists of flow, concentration and phase-field systems. This model represents the dendritic solidification of binary alloys under the action of magnetic field. A numerical scheme using finite element method has been built and its convergence and stability are demonstrated with the help of examples. Realistic numerical simulations of the evolution of a dendrite of Nickel-Copper (Ni-Cu) alloy are presented in an isothermal environment. Finally, the effects of magnetic field on the dendritic evolution have been shown and results are compared with the literature.

Optimum Strategy

Ismat Beg, Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore


I will talk about 2-person zero sum non-cooperative games and use it for successful decision making.

Topsis for Hesitant Intuitionistic Fuzzy Linguistic Term Sets

Tabasam Rashid, Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore


Dealing with uncertainty is a challenging problem, and different tools have been proposed in the literature to deal with it. In this paper, the concept of an hesitant intuitionistic fuzzy linguistic term set is introduced to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible linguistic interval and impossible linguistic interval. Technique for order preference by similarity to ideal solution is proposed in hesitant intuitionistic fuzzy linguistic term set setting for multi-criteria group decision making. An example is given to elaborate the proposed method for the selection of the best alternative.

Least Distance to Consensus Based On Ordered Weighted Averaging Operators

Asma Khalid, Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore

A group based on n decision makers presents their preferences over certain attributes with the help of a fuzzy preference relation. Ordered weighted averaging operators are used to formulate a collective fuzzy preference relation which best represents the choices of the experts. In real life, presuming a consensus among a group of decision makers is an ideal situation and it is rarely attained. Therefore, we seek help from the distance to consensus operator which helps us find the level of satisfaction of the entire group from the collective relation. The lower the distance to consensus, the happier the group is. In the paper presented, we refer to the three consensus types celebrated by the literature. We assert that in practicality, the three consensus types are not achieved which makes it essential to come up with a distance measure to calculate the level of happiness of each expert from the collective relation. Moreover, we compare certain collective relations that are formed using different ordered weighted averaging operators. With the help of such a comparison, a group of experts can choose which ordered weighted averaging operator to use so that the collective relation has least distance to consensus.

Samina Naveed, School of Social Sciences and Humanities, National University of Science and Technology, Islamabad, Pakistan

The paper examines the impact of external financial liberalization on economic growth of Pakistan using multivariate time series analysis. The paper is novel in nature on account of the fact that there is dearth of literature in case of Pakistan for external financial openness and especially any measure to quantify its impact on economic growth. The paper in particular investigates the external financial reform process and captures the external financial liberalization through de facto measures of external financial liberalization. The de facto measure that reflects the actual integration of an economy in international financial markets is captured in the current study as sum of foreign assets and liabilities as a ratio to GDP. The multivariate co integration technique and error correction mechanism is applied to examine the impact of external financial liberalization on economic growth. While controlling for other growth control variables, the results of the paper indicate negative impact of external financial openness on economic growth in long run. This result is in line with majority of international literature evaluating the relationship between external financial openness and economic growth for developing countries.

Issues in Statistical Modeling of Human Capital and Economic Growth Nexus: A Cross Country Analysis

Verda Salman, Department of Economics, School of Social Sciences and Humanities, National University of Sciences and Technology, Islamabad

Muhammad Zahid Siddique, Department of Economics, School of Social Science and Humanities, National University of Sciences and Technology, Islamabad

This paper argues that the disagreements among economists are much deeper than they usually conceive. These disagreements are spread over the entire spectrum of scientific theorization; i.e. explanation, prediction and control (policy) aspects of economics. Economists disagree not merely because their understanding about economic functioning is (for some reasons) imperfect nor because their econometric tool-kit of verifying their theories is limited; instead several deeply rooted reasons leave them divided on matters of economic theory and policy—reasons such as differences over political philosophies, assumptions regarding the nature and working of market economies, approach to scientific methodologies, modeling / estimation techniques and, of course, value-judgments. We argue that disagreements among economists are so deeply rooted due to these reasons that they become almost irreconcilable—no future developments in economic theorization or estimation techniques can eliminate these differences. Economics, like any other science, will continue as a rhetoric activity where different economists make use of authorities, stories, logic and metaphor (e.g. models) to persuade each other.