Books

• Linear Algebra and Optimization for Economists - Submitted to Fondo Editorial PUCP
  Jorge Chávez and Marcelo Gallardo. Foreword by Professor Cesar Martinelli.
  Summary | Index

  Pre-published book about Linear Algebra and Static Optimization for Economists. Covers topics such as convex analysis, constrained optimization, and economic applications.
• Dynamical Systems and Optimal Control for Economists - Under review
  Jorge Chávez and Marcelo Gallardo.
  Summary | Index

  Working book about Dynamical Systems and Optimal Control in Continuous Time for Economists. Topics include differential equations, optimal control theory, and economic models.

Lecture Notes

• Fundamentals of Econometric Theory - Published at Decon PUCP
  Juan Leon Jara-Almonte and Marcelo Gallardo.
  Summary | Lecture Notes

  These lecture notes offer a deep dive into econometrics, structured around key themes from matrix algebra basics to statistical models. The content begins with foundational matrix operations and their relevance to econometrics, advancing to multivariate models with a focus on linear models and optimization issues. It also addresses qualitative variables, sampling methods, and experimental designs. Crucial econometric challenges such as multicollinearity, parameter stability, heteroscedasticity, and serial autocorrelation are thoroughly examined, alongside detection and correction techniques. The notes culminate in discussions on more advanced topics like instrumental variables, maximum likelihood estimation, and an appendix on probability theory, equipping readers with a broad understanding of econometric analysis and application. **New:** The second version will include more examples and an introduction to time series.
• Notes on Optimal Transport Theory and its Applications in Economics and Finance
  Marcelo Gallardo and Carlos Cosentino. Final project for the course Introduction to Optimal Transport, taught by Johel Beltrán.
  Summary | Lecture Notes

  This document discusses applications of optimal transport theory in economics and finance, with a focus on computational methods like entropic regularization and the Sinkhorn-Knopp algorithm. It covers topics such as matching markets stability, cost structure estimation, Credit Value Adjustment, and risk measures, aiming to provide detailed explanations and translations of complex results for students with a strong mathematical background. The document includes an appendix to support understanding and is intended for advanced students interested in economic and financial applications of optimal transport.
• About Brouwer Fixed Point Theorem and its Application in General Equilibrium
  Marcelo Gallardo, Carlos Cosentino, and Eduardo Llamoca.
  Summary | Lecture Notes

  We develop a path towards the proof of Brouwer's Fixed Point Theorem and present an application in economic theory: the existence of the Walrasian Equilibrium. Our goal is to provide the simplest, or at least one of the simplest, proofs for Brouwer's Fixed Point Theorem. The only requirements are real analysis and general topology. Besides one Lemma which is not proved in its most general case, we prove all the results building up to the main theorem. It is important to emphasize that this work does not introduce any new results in the literature. Instead, we focus on developing a clear and understandable approach to Brouwer's Fixed Point Theorem and its applications in general equilibrium.