Events
Department of Mathematics and Statistics
Texas Tech University
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a non-zero drift governed by an independent finite-state Markov chain. Given that the position of the Brownian particle is being observed in real time, the problem is to detect the time at which a coordinate process gets the drift as accurately as possible. This is the so-called quickest real-time detection problem of a Markovian drift. The motivation for a Markovian drift stems from the consideration of a switching environment in practical problems in finance, engineering and other areas. To solve such problem, our main efforts are devoted to solving an equivalent optimal stopping problem with respect to a regime switching diffusion. Our result shows that the optimal stopping boundary can be represented as a unique solution to a non-linear integral equation in some admissible class. This is a joint work with Professor Philip Ernst at Rice University.
This Job Candidate Colloquium is sponsored by the Statistics seminar group, and you are invited to attend Monday the 25th at 4 PM CDT (UT-5) via this Zoom link.
To slow the spread of COVID-19, many countries initially implemented interventions against the disease, such as limiting contacts and mask-wearing. However, approximately 7% of the population have a disability requiring assistance from home care aides to assist with activities of daily living and thus contact-limiting applies differently to these groups. In this talk, we look into an agent-based network model of COVID-19 and the effects of various interventions upon the disabled and care aide communities. Our model accounts for multiple disease compartments, including allowing for asymptomatic transmission; different types of contacts and associated risks; and different contact distributions based on an individual’s occupation. Our work suggests that care aides and disabled people are strongly affected by global intervention strategies and that care aides may be one of the most influential groups in spreading the illness to disabled people and many members of the general population.
Dr. Lindstrom's Job Candidate Colloquium is sponsored by the Applied Math and BioMath seminar groups. Please virtually attend Wednesday the 27th at 3 PM CDT (UT-5) via this Zoom link.
We introduce the flexibility program originally proposed by A. Katok and discuss first results and open questions. Roughly speaking, the aim of this program is to study natural classes of smooth dynamical systems and to find "constructive tools" to freely manipulate dynamical and geometric data inside a fixed class. We will illuminate the connections between flexibility and rigidity phenomena.
Dr. Erchenko's Job Candidate Colloquium is sponsored by the PDGMP seminar group, and you are invited to attend Wednesday the 27th at 4:00 PM CDT (UT-5) via this Zoom link.
Abstract pdf
This Job Candidate Colloquium is sponsored by the Applied Math seminar group, and may be attended Thursday the 28th at 3:15 PM CDT (UT-5) via this Zoom link.
We consider sewing machinery between finite difference and analytical solutions defined
at different scale: far away and near source of the perturbation of the flow.
One of the essences of the approach is that coarse problem and boundary value problem
in the proxy of the source model two different flows. We are proposing method to glue
solution via total fluxes, which is predefined on coarse grid. It is important to mention
that the coarse solution "does not see" boundary.
From industrial point of view our report can be considered as a mathematical shirt on
famous Peaceman well-block radius formulae and can be applied in much more general scenario.
This report presents ongoing project with Daniil Anikeev, Ilya Indrupunski and Ernest Zakirov - group of
applied mathematicians from Russian Academy of Science and student Jared Cullingford from Texas Tech university.
We will also formulate several topics/problems, some time in form of conjecture in harmonic analysis relating to Green function and capacity.
To join the talk on Zoom please click
here.
Abstract: We investigate whether fitting errors of equity-option-implied volatility surfaces are informative
about intermediary frictions.
Relating observed implied volatilities to a smoothed volatility surface,
we find that this error metric increases in idiosyncratic stock volatility and measures of option and stock illiquidity.
An aggregation across the stock universe adds valuable information and the resulting overarching measure of volatility
noise peaks during market distress, exhibits sensible correlations to economic state variables,
and reveals a close link to intermediary equity and debt constraints.
In line with intermediary asset pricing, we find that volatility noise is informative for the cross-sectional variation
in expected returns beyond the equity option market.
This is joint work with Michael Hofmann.
Brief Bio: Marliese Uhrig-Homburg is a professor of finance at the Karlsruhe Institute of Technology (KIT)
in Germany, holding the Endowed Chair (DZ BANK) of Financial Engineering and Derivates.
She obtained a doctoral degree from University of Mannheim and completed her habilitation on “The cost of debt,
credit risk, and optimal capital structure” in 2001.
Her research focuses on the pricing and the role of derivatives, credit risk, fixed income and energy markets,
and the interaction between investment and financing decisions.
She is the author of several recent papers on financial engineering in leading academic journals, among others in the
Journal of Finance, Journal of Corporate Finance, Journal of Banking and Finance, Review of Derivatives Research and
Journal of Environmental Economics and Management.
She is member of the Advisory Board of the German Finance Association (DGF),
co-organizes the triannual international Symposium on Finance, Banking and Insurance in Karlsruhe,
and is vice-speaker of the section Banking and Finance of the German Academic Association for Business Research (VHB).
Since 2008 she serves as vice-dean of the department of Economics and Business Engineering at KIT.
 | Tuesday
Oct. 26
3:30 PM
MATH 016
|
| Real-Algebraic Geometry
Stalks 2
David Weinberg
Department of Mathematics and Statistics, Texas Tech University
|
N/A
We present some optimal control work on mosquito-borne diseases: Malaria and West-Nile Virus. First, a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes is formulated. We derive the basic reproduction number of the infection. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived, and the characterization of the optimal controls are established. We quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission.
Secondly, we consider a West-Nile Virus transmission model that describes the interaction between bird and mosquito populations (eggs, larvae, adults) and the dynamics for larvicide and adulticide, with impulse controls. We derive the basic reproduction number of the infection. We reformulate the impulse control problems as nonlinear optimization problems to derive adjoint equations and establish optimality conditions. We formulate three optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with (1) the benefit of reducing the number of mosquitoes, (2) the benefit of reducing the disease burden, or (3) the benefit of preserving the healthy bird population. Numerical simulations are provided to illustrate the results of both models.
Please virtually attend this week's Biomath seminar at 3:30 PM (UT-5) on Tuesday the 26th via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
The graded deviations $\varepsilon_{ij}(R)$ of a graded ring $R$
record the vector space dimensions of the graded pieces of a certain
Lie algebra attached to the minimal resolution of the quotient of $R$
by its homogeneous maximal ideal. Vanishing of deviations encodes
properties of the ring: for example, $\varepsilon_{ij}(R)= 0$ for
$i\geq3$ if and only if $R$ is complete intersection and, provided $R$
is standard graded, $\varepsilon_{ij}(R)$ whenever $i$ is not equal to
$j$ implies R is Koszul. We extend this fact by showing that if
$\varepsilon_{ij}(R)=0$ whenever $j$ and $i\geq3$, then $R$ is a
quotient of a Koszul algebra by a regular sequence. This answers a
conjecture by Ferraro.
Join the seminar via this Zoom link
Abstract: We study equity return jump risk for a large sample of emerging and developed markets,
by using an analytical framework that endogenously differentiates between jumps and smooth variation.
Jump-size characteristics and jump risks are heterogeneous across equity markets.
Average jump size tends to be larger, while average jump intensity is typically lower for emerging than for developed markets.
We find that international jump risks exhibit strong commonality: The first principal component explains over 60% of
their variation. Its correlation with VIX exceeds 0.7.
Jumps' contribution to total return variability spikes at times of heightened volatility and is typically higher for emerging
than for developed markets.
Individual markets' jump risks have statistically- and economically-significant relationship with VIX,
while local variables do not seem to be uniformly important for jump risks' dynamics.
This is joint work with Mehmet Ozsoy.