Professor: Zhongyi Yuan, Associate Professor of Department of Risk Management, Smeal College of Business - The Pennsylvania State University

Education:

Ph.D., Statistics with concentration in Actuarial Science/Financial Mathematics, University of Iowa.M.S., Statistics, Academy of Mathematics and Systems Science, Chinese Academy of SciencesB.S., Computer Science, Beijing Normal University

Professional Membership:

Associate of the Society of Actuaries (ASA), 2016–PresentMember of American Risk and Insurance Association (ARIA)

Research Interest:Catastrophe risk modelingInsurance-linked securitiesExtreme value theoryStochastic dependenceRare event simulation

Start and end date: Monday July 12th and Wednesday July 21st.

Schedule: Monday to Saturday (6:00 p.m.-09:00 p.m.) Colombia time.

Program details:

This course covers the basics of property & casualty (P&C) insurance as well as actuarial concepts and models for P&C insurance. Its goal is to teach

students the steps for the modeling and estimation processes and how to apply these steps in a business context. Specially, the course covers various

models for loss frequency, loss severity, and aggregate losses that are important for P&C insurance applications. It discusses model estimation

methods that are tailored to the possibly truncated or cencored data from P&C insurance policies, as well as model evaluation and selection methods.

It also teaches the use of credibility theory for loss estimation. Prior knowledge of probability and mathematical statistics is expected.

What you'll learn:

Students will learn various models for loss frequency, loss severity, and aggregate losses that are important for P&C insurance applications. Students will learn model estimation methods and model evaluation and selection methods. Students will learn the use of credibility theory for loss estimation.

24 – hour course 100% virtual Investment: COP $1.500.000

Basics of Property and Casualty Insurance

Basic Distributional Quantities:

Moments, generating functions, and percentilesTails of distributions.Risk measures, such as Value at Risk and Tail Value at Risk.

Actuarial Models:

Data-dependent distributions.Models for loss severities.Models for loss frequencies.Effects of coverage modifications.Aggregate loss models.

Model Estimation:

Basics of point estimate, interval estimate, and hypothesis testingMaximum likelihood estimation (MLE) for individual data, grouped data,complete data, and truncated or cencored data.Variance and interval estimation for MLEs.Bayesian methods.

Model Selection:

Empirical models, kernel density models.Kolmogorov-Smirnov test, Chi-square test, and likelihood ratio testScore-based approaches.

Credibility:

Limited fluctuation credibility, full credibility criterion, partial credibility.Bayesian methodology.Credibility premium.The Buhlmann model and Buhlmann-Straub model.Exact credibility.

Topics covered:

Profesor: Julián Sánchez es magíster en finanzas cuantitativas (2019) y en docencia de las matemáticas (2010). Actualmente, adelanta estudios dedoctorado en economía y es asistente graduado de la Universidad del Rosario. Ha sido profesor de varios cursos en las áreas de programación ymatemáticas, y sus intereses de investigación están en el área de finanzas.

Fecha de inicio y fin: martes 01 de junio y viernes 09 de julio de 2021

Horario: martes a viernes de 6:00 p.m. a 8:00 p.m.

Detalle del programa:

La aleatoriedad juega un papel fundamental en finanzas y economía, en gran parte como consecuencia del riesgo e incertidumbre inherentes en losprecios de los activos en un mercado financiero y en las decisiones de consumo e inversión de los diferentes agentes económicos. Es por esto que lateoría de la probabilidad y los procesos estocásticos constituyen el lenguaje natural para formular y resolver problemas en teoría financiera moderna.

El objetivo de esta asignatura es profundizar conocimientos previamente adquiridos en el área de probabilidad mediante un tratamiento más rigurosoy formal, e introducir al estudiante fundamentos de programación en el lenguaje Python. Los estudiantes usarán esta herramienta para implementar eilustrar computacionalmente técnicas como generación de números aleatorios, representaciones gráficas y métodos de simulación de Monte Carlo. Seintroducirán también definiciones básicas de procesos estocásticos y teoría de martingalas.

Qué aprenderás:

Distinguir conceptos básicos de probabilidad intermedia: espacios de probabilidad discretos, variables aleatorias, sigma-álgebras y espacios deprobabilidad generales. Probabilidad condicional. Distribuciones conjuntas, marginales y condicionales. Convergencia de variables aleatorias.

Entender y usar adecuadamente herramientas analíticas básicas de la creación de modelos estocásticos que luego serán empleadas en lamodelación de variables económicas y financieras.

Comprender conceptos básicos relacionados con la formulación matemática de procesos estocásticos tales como estructuras de información ofiltraciones, esperanza condicional, caminata aleatoria, martingalas y procesos markovianos.

Conocer y usar correctamente herramientas básicas de probabilidad y computación.

Desarrollar programas simples que involucren los métodos específicos vistos en clase.

Analizar y proponer soluciones a problemas de probabilidad y procesos estocásticos, ya sean de forma cerrada o aproximada.

Definir caminata aleatoria. Identificar condiciones bajo las cuales una caminata aleatoria es simétrica y martingala.

48 – horas de clase 100% virtual Investment: COP $3.000.000

Introducción y motivación.

Probabilidad discreta. Estructuras de información en espacios discretos.Variables aleatorias. Función de distribución. Distribuciones discretas,continuas y mixtas. Valor esperado y varianza. Distribuciones deprobabilidad de uso frecuente.

Generación de números aleatorios.

Vectores aleatorios. Distribuciones conjuntas multivariadas.Distribuciones marginales. Distribuciones condicionales. Covarianza ycorrelación.

Valor esperado condicional con respecto a eventos y a variablesaleatorias.

Contenido del curso:

Espacios de probabilidad generales. Probabilidad condicional. Eventos independientes.

Procesos estocásticos en tiempo discreto. Caminatas aleatorias. Simulación.

Martingalas en tiempo discreto.

Movimiento Browniano. Procesos de Poisson.

Variación cuadrática. Fórmula de Itô básica y diferencial estocástica. Modelo de Black-Scholes.

Professor: Eduardo Ferraz Castelo Blanco Ferreira, Principal Professor at the Faculty of Economics of the Universidad del Rosario. He is a Ph.D. inEconomics from Sao Paulo School of Economics-FGV (Brazil). Additionally, he has a Ph.D. in Mathematics from Telecom Paris Tech in France. His areas ofinterest are: Crime Economics and Political Economy.

Start and end date: Wednesday June 02nd and Friday July 16th.

Schedule: June days - 2,4,8,9,11,15,16,18,21,23,24,25,28,30 and July days - 1,2,6,7,8,9,12,14,15,16 (09:00 a.m. – 11:00 a.m.) Colombia time.

Program details:

This course is aimed for master students preparing for a PhD in Economics in a top program and PhD students in Economics. The purpose of the courseis to provide tools of real analysis used in economic research and to improve analytical reasoning. At the end of the course, students are moreproficient in dealing with mathematical structures behind economic models, in expressing themselves in the mathematical language, and inunderstanding advanced research papers relying on real analysis arguments.

What you'll learn:

Students are more proficient in dealing with mathematical structures behind economic models. Students are more proficient in expressing themselves in the mathematical language. Students are more proficient in understanding advanced research papers relying on real analysis arguments.

The 8 first sessions should cover the contents up to differentiability on the real space.

Sections 9-16 are aimed to cover from metric spaces until correspondences.

Sections 17-24 are supposed to cover applications on Nash equilibria, Dynamic programming, and Linear Algebra.

Sessions 25-32 deals with the remaining contents of the course. It is expected that students are autonomously to apply the tools presented inclass to solve the problem sets. Students will receive the lecture notes (slides and complementary material) and the problem sets 1-2 weeksbefore the content is presented.

Topics covered:

48 – hour course 100% virtual Investment: COP $3.000.000