
Caitlin M. Davis
University of WisconsinMadison, USA

Laura A. LeGare
University of Notre Dame, USA

Cory W. McCartan
Harvard University, Cambridge, USA

Luke G. Rogers
University of Connecticut, Storrs, USA
 DOI 10.4171/JFG/100
 JFG VOL. 8, NO. 2 PP. 117–152
 2018 project page
Author: Alexander Teplyaev
Fractional Gaussian fields on surfaces and graphs
Group Members: Tyler Campos, Andrew Gannon, Benjamin HanzsekBrill, Connor Marrs, Alexander Neuschotz, Trent Rabe and Ethan Winters.
Mentors: Rachel Bailey, Fabrice Baudoin, Masha Gordina
Overview: We will study and simulate on computers the fractional Gaussian fields and their discretizations on surfaces like the twodimensional sphere or twodimensional torus. The study of the maxima of those processes will be done and conjectures formulated concerning limit laws. Particular attention will be paid to logcorrelated fields (the socalled Gaussian free field).
Fair pricing and hedging under small perturbations of the numéraire on a finite probability space
William Busching, Delphine Hintz, Oleksii Mostovyi, Alexey Pozdnyakov
https://msp.org/soon/coming.php?jpath=involve
The Information Premium on a Finite Probability Space
Jake Koerner, Joo Seung Lee, Oleksii Mostovyi
Boxball systems and RSK tableaux
Séminaire Lotharingien de Combinatoire (2021)
Sém. Lothar. Combin. 85B (2021), Art. 14, 12 pp.
Proceedings of the 33rd Conference on Formal Power
Series and Algebraic Combinatorics
Ben Drucker, Eli Garcia, Emily Gunawan, and Rose Silver
A boxball system is a collection of discrete time states representing a permutation,
on which there is an action called a BBS move. After a finite number of BBS moves
the system decomposes into a collection of soliton states; these are weakly
increasing and invariant under BBS moves. The students proved that when this
collection of soliton states is a Young tableau or coincides with a partition of a type
described by RobinsonSchensted (RS), then it is an RS insertion tableau. They also
studied the number of steps required to reach this state.
The financial value of knowing the distribution of stock prices in discrete market models
The financial value of knowing the distribution of stock prices in discrete market models
Ayelet Amiran, Fabrice Baudoin, Skylyn Brock, Berend Coster, Ryan Craver, Ugonna Ezeaka, Phanuel Mariano and Mary Wishart
Vol. 12 (2019), No. 5, 883–899
DOI: 10.2140/involve.2019.12.883
arXiv:1808.03186
project page:
Financial Math: Portfolio Optimization and Dynamic Programming
A derivation of the BlackScholes option pricing model using a central limit theorem argument
Probability, Analysis and Mathematical Physics on Fractals 2018
Each year we are looking for a group of undergraduate students to work on Probability, Analysis and Mathematical Physics on Fractals. The aim of the projects will be exploration of differential equations and various operators on fractal domains. Students in the project are supposed to have the usual background in linear algebra and differential equations. Knowledge of Matlab, Mathematica, other computer algebra systems, or programming, as well as proof writing, mathematical analysis, and probability may be helpful but is not required. Previous undergraduate work includes published papers on the eigenmodes (vibration modes) of the Laplacian (2nd derivative) of functions that live on Sierpinski gasket type fractals, and the electrical resistance of fractal networks, as well as work on Laplacians on projective limit spaces. The exact choice of the topics to study will depend on the students’ background and interests. Besides being interesting, taking part in a research project like this may be very useful in the future (for instance, when applying to graduate schools).
Luke Rogers, Gamal Mograby, Sasha Teplyaev, Patricia AlonsoRuiz
Math UConn REU at JMM 2018
Two of our REU (2017 Stochastics) participants, Raji Majumdar and Anthony Sisti, will be presenting posters Applications of Multiplicative LLN and CLT for Random Matrices and Black Scholes using the Central Limit Theorem on Friday, January 12 at the MAA Student Poster Session, and both of them will be giving talks on Saturday, January 13 at the AMS Contributed Paper Session on Research in Applied Mathematics by Undergraduate and PostBaccalaureate Students.
Their travel to the 2018 JMM has been made possible with the support of the MAA and UConn’s OUR travel grants.
Financial Math: Portfolio Optimization and Dynamic Programming
Group Members
Ayelet Amiran, Skylyn Brock, Ryan Craver, Ugonna Ezeaka, Mary Wishart
Supervisors
Fabrice Baudoin, Berend Coster, Phanuel Mariano
Overview
Financial markets have asymmetry of information when it comes to the prices of assets. Some investors have more information about the future prices of assets at some terminal time. However, what is the value of this extra information?
We studied this anticipation in various models of markets in discrete time and found (with proof) the value of this information in general complete and incomplete markets. For special utility functions, which represent a person’s satisfaction, we calculated this information for both binomial (complete) and trinomial (incomplete) models.
Publication
Journal reference:  Involve 12 (2019) 883899 
DOI:  10.2140/involve.2019.12.883 
arXiv:1808.03186
Presentation
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