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
Dynamical Systems and Optimal Control in Continuous Time for Economists. Topics include linear differential equations, nonlinear dynamical systems, limit cycles, calculus of variations, 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, basic time series analysis, and an appendix on probability theory, equipping readers with a broad understanding of econometric analysis and application.
Game Theory - Notes for 1ECO43 (2025) PUCP
Professor César Martinelli, and written by Marcelo Gallardo.
Summary | Lecture Notes (draft)
These lecture notes offer a deep dive into econometrics, structured around key themes from matrix algebra basics to statistical models.
These lecture notes offer a comprehensive exploration of game theory, structured around both static and dynamic models under varying information environments. The material opens with static games—first with complete information (Nash equilibrium) and then with incomplete information (Bayesian Nash equilibrium)—before moving on to extensive-form games with perfect and imperfect information, examining subgame perfect equilibrium as well as perfect Bayesian and sequential equilibria. It also covers cooperative solution concepts, including the Nash bargaining solution and Rubinstein’s alternating-offers model, and delves into infinitely repeated games with automaton-based strategy representations. An appendix presents decision theory under uncertainty, a proof of the minimax theorem via convex-set separation, and concise overviews of seminal papers by Myerson (1978), Kreps & Scheinkman (1983), Reny (1999), and Echenique & Saito (2015). The core textbook references are Osborne & Rubinstein (1994), Mas-Colell, Whinston & Green (!995), and Fudenberg & Tirole (1991).
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.
Real Business Cycles for 1ECO74 (Macroeconomics, Graduate School)
Marcelo Gallardo, following Paul Castillo’s classes
Summary | Lecture Notes (draft)
Preliminary draft, please notify any mistake!
RBC with productive public investment
Marcelo Gallardo
Summary | Note
Preliminary draft, please notify any mistake!