Quantitative Finance

We study a risk-sharing economy where an arbitrary number of heterogenous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward-backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross-section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study.

These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output matrix model, linear programming, elementary financial mathematics, as well as differential and integral calculus of real-valued functions of one real variable. A special focus is set on applications in quantitative economical modelling.

The Labouchere gambling system is hypothesized to increase the probability of winning a predetermined arbitrary profit in a gambling system such as a coin flip or a roulette game in which both payouts and odds are 1:1. However, use of the system increases the downside monetary risk in the event of a streak of multiple losses. To begin, a player creates an arbitrary series of consecutive integers with a sum equal to the desired profit from multiple rounds of betting. Using the system, a player will either win an amount equal to the sum of the elements of the initial series or lose all of their available capital. This sequence was simulated multiple times to determine the statistical characteristics of both the return and of the loss in an average round of betting. By running the simulations of millions of rounds of Labouchere, it was possible to discern the probable outcomes of running the system using the Labouchere gambling sequence and plotting the results on a graph to map the average return on the initial capital investment. The Labouchere system is very psychologically appealing to players because when applied over time it provides very consistent linear returns. However, there is eventually a critical moment at which the available capital for betting is exceeded and a player loses all of their available capital. It was found that as the number of bets increased, the outcome of applying the sequence approached zero.

This study evaluated the three dimensions of performance of commercial banks in Bangladesh by analyzing the trend of the Malmquist Productivity Index (MPI) of the Total Factor Productivity (TFP), Return on Asset (ROA) and Total Stock Return (TSR) over the period 2011 to 2015. The study developed an empirical framework with the intention to examine the equivalency of three dimensions of performance. Since, the measures of performance are different, they cannot be tested in their original form; hence, the growth rate of each category of performance measures were estimated and tested to examine the comparability among them. Evaluation of profitability revealed a decreasing trend and evaluation of stock performance suggests that investors are incurring losses on their investment over the selected period. Evaluation of productivity indicates that productivity regress was recorded initially but at the end of the studied period a modest productivity growth was recorded. Finally, this study was able to ascertain the anticipated equivalency of outcome of the three dimensions of performance.

This paper presents a Python object-oriented software and code to compute the annual production resilience indicator. The annual production resilience indicator can be applied to different anthropic and natural systems such as agricultural production, natural vegetation and water resources. Here, we show an example of resilience analysis of the economic values of the agricultural production in Europe. The analysis is conducted for individual time-series in order to estimate the resilience of a single commodity and to groups of time-series in order to estimate the overall resilience of diversified production systems composed of different crops and/or different countries. The proposed software is powerful and easy to use with publicly available datasets such as the one used in this study.

In mutual fund, an investment adviser gives advice to clients about investing in securities such as stocks, bonds, mutual funds, or exchange traded funds. Some investment advisers manage portfolios of securities. In this paper, we analyze advisor portfolio for each advisor so as to recognize the pattern in each adviser's portfolio. Such analysis helps the sales people to sell the fund company products to the suitable advisors desirable to the nature of the product they want to sell. This is done by analyzing the kind of products advisors have been interested in which will help to boost the sales of the products as sales people will be reaching the appropriate advisors.

Energy consumption in Ecuador has increased significantly during the last decades, affecting negatively the financial position of the country since large energy consumption subsidies are provided in its internal market and Ecuador is mostly a crude oil exporter and oil derivatives importer country. This research seeks to state the long run price and income elasticities of energy demand in Ecuador, by analyzing information spanning the period from 1970 to 2015. A cointegration analysis and an estimation by using a Dynamic Ordinary Least Squares approach considering structural breaks is carried out. Results obtained are robust and suggest that in the long run energy demand in Ecuador is highly income elastic, has no relationship with its price and has an almost unitary but inverse relationship with the industrial production level. Conclusions and economic policy suggestions are also provided.

The paper proposes a new stochastic intervention control model conducted in various commodity and stock markets. The essence of the phenomenon of intervention is described in accordance with current economic theory. A review of papers on intervention research has been made. A general construction of the stochastic intervention model was developed as a Markov process with discrete time, controlled at the time it hits the boundary of a given subset of a set of states. Thus, the problem of optimal control of interventions is reduced to a theoretical problem of control by the specified process or the problem of tuning. A general solution of the tuning problem for a model with discrete time is obtained. It is proved that the optimal control in such a problem is deterministic and is determined by the global maximum point of the function of two discrete variables, for which an explicit analytical representation is obtained. It is noted that the solution of the stochastic tuning problem can be used as a basis for solving control problems of various technical systems in which there is a need to maintain some main parameter in a given set of its values.

Most of the grand challenges of humanity today involve complex agent-based systems, such as epidemiology, economics or ecology. However, remains as a pending task the challenge of identifying the general principles underlying their self-organizing capabilities. This article presents a novel modeling approach, capable to self-deploy both the system structure and the activities for goal-driven agents that can take appropriate actions to achieve their goals. Humans, robots, and animals are all endowed with this type of behavior. Self-organization is shown to emerge from the decisions of a common rational activity algorithm, based on the information of a system-specific goals dependency network. The unique self-deployment feature of this approach, that can also be applied to non-goal-driven agents, can boost considerably the range and depth of application of agent-based modeling.

Certain theoretical aspects of vector autoregression (VAR) as tools to model economic time series are revised, in particular their capacity to include both short term and long term information. The VAR model, in its error correction form, is derived and the permanent-transitory decomposition of factors proposed by Gonzalo and Granger (1995) studied. An introductory exposition of estimation theory for reduced rank models, necessary to estimate the error correction model, is given. Cointegration analysis using the VAR model is carried out for government bond interest rates (short, medium and long term) of the United States, Mexico and Canada, with the objective of finding the long-term common factors that drive the system. The error correction model of this system is estimated using Johansen's method. Using this estimation the permanent-transitory decomposition of the system is calculated. Hypothesis tests are carried out on permanent factors to determine which of the nine rates studied drive the system.