Events for 03/21/2024 from all calendars

Seminar on Banach and Metric Space Geometry

Time: 10:00AM - 11:00AM

Location: BLOC 302

Speaker: Harisson Gaebler, University of North Texas

Title: Riemann integration and asymptotic structure of Banach spaces

Abstract: Let X be a Banach space. A bounded and Lebesgue almost-everywhere continuous function f:[0,1]\to X is Riemann-integrable. However, the converse statement is false in general. This motivates the following definition: X is said to have the Lebesgue property if every Riemann-integrable function f:[0,1]\to X is Lebesgue almost-everywhere continuous. In this talk, I will discuss my work during the last several years on the relationship between the Lebesgue property and asymptotic structures. I will begin by giving an overview of the Lebesgue property that includes relevant examples, older results, and a brief mention of my first paper on this topic which ultimately led to two more recent joint works. I will then spend the majority of the talk discussing the these two more recent papers whose results include 1) the characterization of the Lebesgue property in terms of a new asymptotic structure that sits strictly between the notions of a unique \ell_{1} spreading model and a unique \ell_{1} asymptotic model (this is a joint work with Bunyamin Sari) and 2) the complete separation of the Lebesgue property from a (uniformly) unique \ell_{1} spreading model (this is a joint work with Pavlos Motakis and Bunyamin Sari). Lastly, I will mention two relevant open problems.

Stochastic Processes Seminar

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Duy Nguyen, Marist College

Title: Continuous-time optimal investment with portfolio constraints: a reinforcement learning approach

Abstract: In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling constraint and borrowing prohibition. The optimal feedback policy of the exploratory unconstrained classical EU problem is shown to be Gaussian. In the case where the portfolio weight is constrained to a given interval, the corresponding constrained optimal exploratory policy follows a truncated Gaussian distribution. We verify that the closed form optimal solution obtained for logarithmic utility \blue{and quadratic utility} for both unconstrained and constrained situations converges to the non-exploratory expected utility counterpart when the exploration weight goes to zero. Finally, we establish a policy improvement theorem and devise an implementable reinforcement learning algorithm by casting the optimal problem in a martingale framework. Our numerical examples confirm the intuitive understanding that a broader domain of investment opportunities necessitates a higher exploration cost. Notably, when subjected to both short-selling and money borrowing constraints, the exploration cost becomes negligible compared to the unconstrained case.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Dr. Alexandru Hening, Texas A&M University, Mathematics

Title: Can environmental fluctuations save species from extinction?

Abstract: In order to have a realistic mathematical model for the dynamics of interacting species in an ecosystem it is important to include the effects of random environmental fluctuations. Many have thought that environmental fluctuations are detrimental to the coexistence of species. However, this is not always the case. I will present to you some interesting examples where environmental fluctuations lead to highly counterintuitive results.