Quantitative Finance

Recently we uploaded to the arxiv a paper entitled: Improving the Economic Complexity Index. There, we compared three metrics of the knowledge intensity of an economy, the original metric we published in 2009 (the Economic Complexity Index or ECI), a variation of the metric proposed in 2012, and a variation we called ECI+. It was brought to our attention that the definition of ECI+ was equivalent to the variation of the metric proposed in 2012. We have verified this claim, and found that while the equations are not exactly the same, they are similar enough to be our own oversight. More importantly, we now ask: how many variations of the original ECI work? In this paper we provide a simple unifying framework to explore multiple variations of ECI, including both the original 2009 ECI and the 2012 variation. We found that a large fraction of variations have a similar predictive power, indicating that the chance of finding a variation of ECI that works, after the seminal 2009 measure, are surprisingly high. In fact, more than 28 percent of these variations have a predictive power that is within 90 percent of the maximum for any variation. These findings show that, once the idea of measuring economic complexity was out, creating a variation with a similar predictive power (like the ones proposed in 2012) was trivial (a 1 in 3 shot). More importantly, the result show that using exports data to measure the knowledge intensity of an economy is a robust phenomenon that works for multiple functional forms. Moreover, the fact that multiple variations of the 2009 ECI perform close to the maximum, tells us that no variation of ECI will have a performance that is substantially better. This suggests that research efforts should focus on uncovering the mechanisms that contribute to the diffusion and accumulation of productive knowledge instead of on exploring small variations to existing measures.

Over a century ago, Oliver Wendell Holmes invited scholars to look at the law through the lens of probability theory: "The prophecies of what the courts will do in fact, and nothing more pretentious, are what I mean by the law." Yet few legal scholars have taken up this intriguing invitation. As such, in place of previous approaches to the study of law, this paper presents a non-normative, mathematical approach to law and the legal process. Specifically, we present a formal Bayesian model of civil and criminal litigation, or what we refer to as the litigation game; that is, instead of focusing on the rules of civil or criminal procedure or substantive legal doctrine, we ask and attempt to answer a mathematical question: what is the posterior probability that a defendant in a civil or criminal trial will be found liable, given that the defendant has, in fact, committed a wrongful act?

This paper explores the possible contextual factors that drove some individuals to lead, and others to join the pro-secessionist rebellion in the 2013-2014 conflict in Eastern Ukraine. We expand on the existing rational choice literature on revolutionary participation and rebellious movements by building a contextual choice model accounting for both cost-benefit and behavioral considerations taken by Pro-Russian militants and rebels in the region of Donbass. Our model generates predictions about the characteristics of the socio-political-cultural context that are most likely to ignite and sustain hierarchical rebel movements similar to those in Ukraine.

The Humber region in the UK is a large and diverse industrial area centred around oil refining, chemical industries and energy production. However there is currently a desire to see the region transition towards a more bio-based economy. New bio-related industries are being situated in the region as a consequence of policy and economic incentives. Many of these industries are connected through their supply chains, either directly, or by sharing common suppliers or customers and the growth or decline of one industry can hence have impacts on many others. Therefore an important question to consider is what effect this movement towards bio-based industry will actually have on the regional economy as a whole. In this paper we develop a general abstract dynamical model for the metabolic interactions of firms or industries. This dynamical model has been applied to the Humber region in order to gain a deeper understanding of how the region may develop. The model suggests that the transition to a bio-based economy will occur with oil refining losing its dominance to bioethanol production and biological chemical production, whilst anaerobic digestion grows as a major source of electricity, in turn driving up the value of regional waste aggregators and arable farming in the overall economy.

We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are parsimonious in form and easy to execute, as they are both oblivious of past history and blind to other players' present states. Our transient results can be extended to a stationary case, where the finite counterparts are special discounted stochastic games. The kind of equilibria we adopt for SSNG are similar to distributional equilibria that are well understood in literature, and they themselves are shown to exist.

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, there has not been a full investigation of evolving world economic networks with Markov chain formalism. Using the recently available world input-output database, we modeled the evolution of the world economic network from 1995 to 2011 through analysis of a series of finite Markov chains. We assessed different aspects of this evolving system via different properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average monetary flow.

The paper models foreign capital inflow from the developed to the developing countries in a stochastic dynamic programming (SDP) framework. Under some regularity conditions, the existence of the solutions to the SDP problem is proved and they are then obtained by numerical technique because of the non-linearity of the related functions. A number of comparative dynamic analyses explore the impact of parameters of the model on dynamic paths of capital inflow, interest rate in the international loan market and the exchange rate.

We present a discrete-time dynamic model of income tax evasion. The model is solved exactly in the case of a single taxpayer and shown to have some realistic properties, including avoiding the Yitzhaki paradox. The extension to an agent-based model with a network of taxpayers is also investigated.

This paper investigates an infinite-horizon problems in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak. It is shown that optimal solutions a class of problems raising from time inconsistency problems in the framework of the neoclassical one-sector model of economic growth, and contains new results in environment economics. Without exogenous commitment mechanism, a notion of the equilibrium strategies instead of the optimal strategies is introduced. We characterized the equilibrium strategies by an integro-differential equation system. For two special criteria, the bi-exponential criteria and the Chichilnisky criteria, we established the existence of the equilibrium strategies.

Credit estimation and bankruptcy prediction methods have been utilizing Altman's z score method for the last several years. It is reported in many studies that z score is sensitive to changes in accounting figures. Researches have proposed different variations to conventional z score that can improve the prediction accuracy. In this paper we develop a new multivariate non-linear model for computing the z score. In addition we develop a new credit risk index by fitting a Pearson type-III distribution to the transformed financial ratios. The results from our study have shown that the new z score can predict the bankruptcy with an accuracy of 98.6% as compared to 93.5% by the Altman's z score. Also, the discriminate analysis revealed that the new transformed financial ratios could predict the bankruptcy probability with an accuracy of 93.0% as compared to 87.4% using the weights of Altman's z score.