Mathematics Colloquium

Add to Calendar 12/07/2017 15:35:0011/09/2017 16:30:0015Mathematics ColloquiumSpeaker One: Kaity Jones, University of Dayton Host: Peter Hovey Title: The Search for an Improved Estimator in Determining the Probability of Jet Engine Failure Abstract: There are many circumstances under which a jet engine might fail, including the introduction of foreign objects, the development of cracks in the engine, and when these combine, a build-up of harmonic frequencies know as High Cycle Fatigue that can cause the engine to rattle apart. The goal of this paper is to create a new, more accurate estimator for the probability of engine failure using a transformation of the performance function with probability of failure based on Gumbel’s extreme value distribution. These probabilities are then compared to their binomial counterparts in an effort to determine if an estimator can be found which reduces the bias inherent in maximum likelihood estimation and provides the accuracy of Monte Carlo simulations without the need for billions of trials to be run to achieve accurate estimation of probabilities as small as one in a million. Speaker Two: Runze Hu, University of Dayton Host: Dan Ren Title: Optimal stopping problems for a Brownian motion with a disorder on a finite interval Abstract: In this project, I will consider the optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. The optimal stopping rules are found as the first hitting time of the Shiryaev-Roberts statistic to time-dependent boundaries. Also, I will apply the continuous time stochastic process model to the stock of AAPL from various time in 2011-2017. The basic idea is that there is a fast rate of growth in price, then a peak and then a fast decline. I will try to use the model to simulate the exit time near the peak in prices or valley of its short position. Refreshments are available at 3:00 PM in SC 313F. The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. Science Center Room 323Paul Eloepeloe1@udayton.eduNo12/07/2017

Thursday, December 7

Time: 3:35 p.m. — 4:30 p.m.

Location: Science Center Room 323

Tags:  Colloquia, Mathematics, Sciences

Cost:  Free

Speaker One: Kaity Jones, University of Dayton

Host: Peter Hovey

Title: The Search for an Improved Estimator in Determining the Probability of Jet Engine Failure

Abstract: There are many circumstances under which a jet engine might fail, including the introduction of foreign objects, the development of cracks in the engine, and when these combine, a build-up of harmonic frequencies know as High Cycle Fatigue that can cause the engine to rattle apart. The goal of this paper is to create a new, more accurate estimator for the probability of engine failure using a transformation of the performance function with probability of failure based on Gumbel’s extreme value distribution. These probabilities are then compared to their binomial counterparts in an effort to determine if an estimator can be found which reduces the bias inherent in maximum likelihood estimation and provides the accuracy of Monte Carlo simulations without the need for billions of trials to be run to achieve accurate estimation of probabilities as small as one in a million.

Speaker Two: Runze Hu, University of Dayton

Host: Dan Ren

Title: Optimal stopping problems for a Brownian motion with a disorder on a finite interval

Abstract: In this project, I will consider the optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. The optimal stopping rules are found as the first hitting time of the Shiryaev-Roberts statistic to time-dependent boundaries. Also, I will apply the continuous time stochastic process model to the stock of AAPL from various time in 2011-2017. The basic idea is that there is a fast rate of growth in price, then a peak and then a fast decline. I will try to use the model to simulate the exit time near the peak in prices or valley of its short position.

Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. 

Contact Information:

Name:  Paul Eloe
Email:  peloe1@udayton.edu