The Department of Finance and Risk Engineering welcomes Alejandra Quintos Lima from Columbia University to the BQE Lecture Series.
Dependent Stopping Times and an Application to Credit Risk Theory
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 derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show 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.
Alejandra is finishing her Ph.D. in Statistics at Columbia University under the direction of Prof. Philip Protter. Her research interests lie primarily in problems in probability, stochastic processes, and statistics motivated by their applications, particularly those applications in mathematical finance. During her Ph.D. program, Alejandra held a Fulbright grant, and she was one of the finalists for the 2021 Presidential Awards for Outstanding Teaching by a Graduate Student at Columbia University. Before graduate school, she worked for Citigroup in Mexico, participated in a summer research program at Cornell University, and did an internship in DC. She held a merit scholarship to major in Actuarial Sciences in UDLAP (Puebla, Mexico) where she graduated as Summa Cum Laude and was the Valedictorian of her class.