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DTSTAMP:20261015T101334
DTSTART;TZID=America/Detroit:20261021T160000
DTEND;TZID=America/Detroit:20261021T170000
SUMMARY:Lecture / Discussion:Probability and Analysis Seminar: Small Moments of the Sensitivity of Polynomial Threshold Functions
DESCRIPTION:Abstract: Polynomial threshold functions (PTFs) are a central class of Boolean functions with important roles in learning theory and approximation. A fundamental question is to understand the complexity of their behavior under small perturbations of the input. On the Boolean cube\, this is captured by notions such as sensitivity\, average sensitivity\, and Boolean surface area. In this talk\, we revisit a recursive approach used to derive bounds for the average sensitivity and Boolean surface area of PTFs and obtain a polylogarithmic bound for small moments of their sensitivity. We will also explore the interplay between Fourier expansion and induction on scales from harmonic analysis\, random averaging from probability\, and decision trees and regularization from combinatorics.
UID:153329-21915644@events.umich.edu
URL:https://events.umich.edu/event/153329
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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DTSTAMP:20261006T181240
DTSTART;TZID=America/Detroit:20261021T160000
DTEND;TZID=America/Detroit:20261021T170000
SUMMARY:Workshop / Seminar:Stochastic Models and Optimization for Dynamic Portfolio Management: A Compartment Framework for Financial Growth and Decision Support
DESCRIPTION:Portfolio management is a dynamic decision-making problem characterized by uncertainty\, evolving asset states\, competing risk–return objectives\, and changing market conditions. This research develops an integrated stochastic and optimization framework for modelling financial growth and formulating investment policies by representing a portfolio as a dynamic compartmental system in which risky and non-risky assets undergo stochastic growth\, loss\, transformation\, and migration. Univariate and bivariate birth–death and migration processes\, together with Markov and hidden-state modelling perspectives\, are employed to characterize the probabilistic evolution and interactions of portfolio components.\n\nThe proposed framework systematically connects stochastic process modelling\, probability analysis\, statistical inference\, nonlinear optimization\, computational analysis\, and decision support. Difference and differential equations are developed to describe portfolio dynamics\, while probability-generating functions and moment-based methods are used to derive expectations\, variances\, covariances\, and related measures under transient and steady-state conditions. These statistical characteristics subsequently serve as inputs to stochastic optimization models that address alternative investment objectives\, including risk control\, volatility management\, portfolio diversification\, and the determination of appropriate investment policy parameters.\n\nComputational experimentation and sensitivity analysis are incorporated to examine the effects of growth\, loss\, and transformation parameters on portfolio behavior\, using real-world financial data to ground empirical exploration and model validation. The resulting framework provides a pathway from uncertainty modelling to quantitative risk assessment\, prescriptive optimization\, and intelligent decision support. The research is intended to stimulate interdisciplinary collaboration across Statistics\, Stochastic Processes\, Mathematical Finance\, Operations Research\, Optimization\, Data Science\, and Computational Modelling\, with potential applications in real-data validation\, software development\, joint publications\, and future research on scalable stochastic decision-support systems for contemporary financial management.
UID:153381-21915734@events.umich.edu
URL:https://events.umich.edu/event/153381
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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