Graduate Student Seminar

Speaker 1: Hyekyung Park

Title

Robust Value-at-Risk (VaR) Portfolio Selection

Abstract

Consider a single period portfolio selection problem that maximizes return and has a probability of losing at most $δ money (bounded by ε). The probability can have any distribution p in P, and the set of all distributions that have average return μ and covariance Σ. We can find μ and Σ by using the historical price of the assets on Google Finance. To solve the problem, we can use the optimization model using a new parameter introduced by Bertsimas and Sim (2004), and estimate the risk level relevant to the new parameter. To offer a numerical example, we will make a portfolio consisting of 6 assets, AAPL, V, PFE, IBM, KMB, MCD, for the next 6 months between Jan, 01, 2014 and June, 30, 2014 by using this model. Our goal will be to see how much return we get.

Speaker 2: Nicole Massarelli

Title

Effects of Sensory Perturbations on the Lamprey Central Pattern

Abstract

Sensory feedback plays a large role in regulating vertebrate locomotion.  We investigate the effects of sensory perturbation on the lamprey central pattern generator (CPG).  The lamprey CPG is a neural circuit in the spinal cord that produces a traveling wave of neural activity which activates muscles for swimming. Sensory feedback in the lamprey spinal cord comes from edge cells, which are neurons located in the margin of the spinal cord. Edge cells detect stretch and rate of stretch, and provide feedback to the CPG. Previously, we have studied the entrainment ranges of the CPG, both experimentally and mathematically. Entrainment describes the phenomena where the CPG will match the frequency of an applied stimulus if it is close to its natural frequency.  To investigate how perturbations affect entrainment, we add Gaussian band-limited white noise to the edge cell connections in our CPG model.   Correspondingly, we add the same noise to the bending signal in the experimental set-up.  In both cases, the CPG is extremely robust to noise and can produce stable swimming patterns for a wide range of noise levels.  This analysis is the precursor to harmonic transfer function analysis of white noise perturbations which will allow us to non-parametrically identify the relationship between the noisy input signal and the CPG output. Eventually, we will be able to predict the effects of perturbations on closed-loop swimming.