# Alejandra Quintos (University of Wisconsin–Madison)

Date

Friday February 17, 20232:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234## Math & Stats Department Colloquium

**Friday, February 17th, 2023**

**Time:** 2:30 p.m. **Place:** Jeffery Hall, Room 234

**Speaker:** Alejandra Quintos (University of Wisconsin–Madison)

**Title:** Dependent Stopping Times and an Application to Credit Risk Theory

**Abstract:** Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.

In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We show the impact of increasing the number of G-SIBs and that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.

We end the talk with some related and outgoing work that uses phase-type distributions.

This talk is based on joint work with Philip Protter, Robert Jarrow, Jianxi Su, and Yisub Kye.

Alejandra is an Assistant Professor and a Nellie McKay Fellow in the Department of Statistics at the University of Wisconsin-Madison. She completed her Ph.D. in Statistics at Columbia University where she held a Fulbright grant and received the Howard Levene Outstanding Teaching Award. Before graduate school, Alejandra had a merit scholarship to major in Actuarial Sciences at Universidad de las Américas Puebla from where she graduated Summa Cum Laude and was the Valedictorian of her class. Her research interests include problems in probability, stochastic processes, and statistics motivated by their applications, particularly in mathematical finance and more specifically in credit risk theory.