Congestion and Penalization in Optimal Transport - Submitted Marcelo Gallardo, Manuel Loaiza, and Jorge Chávez.
Abstract | Pre-print
In this paper we introduce two novel models derived from the discrete optimal transport problem. The first model extends the traditional transport problem by adding a quadratic congestion factor directly into the cost function, while the second model replaces conventional constraints with weighted penalization terms. We present theoretical results, for the characterization of interior and corner solution for some specific cases, and we perform smooth comparative statics analysis. We also propose an O((N+L)(NL)2) algorithm for computing the optimal plan for the penalized model assuming interior solutions. Pre-print in arXiv differs slightly from the last version in SSRN.
Heterogenous Quadratic Regularization in Optimal Transport - Submitted Marcelo Gallardo, Manuel Loaiza and Jorge Chávez.
Abstract | Pre-print available under request
In this paper, we build upon the optimal transport quadratic regularization model to develop a framework that incorporates congestion costs, particularly in matching within the healthcare and education sectors. Specifically, we introduce a model with heterogeneous quadratic costs. We analyze the model's properties under specific cases, extending the existing literature. Furthermore, we explore key structural characteristics of the model and provide numerical examples illustrating why this formulation more accurately captures real-world phenomena, particularly in the Peruvian context. The main result consists of identifying a specific type of corner solution when matching the same number of clusters, i.e., N=L.
Irregular wave dynamics driven by a random force within the Burgers equation - Submitted
Marcelo Gallardo and Marcelo Flamarion.
Abstract | Pre-print under request
In this article, we study the classical Burgers equation as a model for random fields. First, we consider initial data defined as a sum of harmonics with random phases and compute the blow-up time. Several simulations are performed, revealing that, while the critical blow-up time is approximately distributed according to a Gaussian law, the statistical tests reject the normality hypothesis. For the viscous case, we analyze waves driven by a random force. Using the Cole-Hopf transformation, the averaged wave field is computed numerically. Through a change of variables, we demonstrate that randomness primarily affects the phase of the wave field. Assuming the phase follows a uniform distribution, we show that the averaged field spreads and diminishes over time.
Working Papers
Political and economic uncertainty indicator for Peru based on Twitter and GPT-3.5 Turbo - New version coming soon Manuel Loaiza, Marcelo Gallardo, and Gabriel Rodriguez.
Abstract | Draft available under request
This paper develops a new political-economic uncertainty index based on tweets from influential figures in Peruvian politics and economics. Tweets are analyzed using GPT-3.5 Turbo, generating a time series of political-economic uncertainty.
Field Experiments on Seasonal Products and Markdown Pricing
Marcelo Gallardo and Carlos Noton.
Abstract | Coming soon