Department of Mathematics

In this talk, we will go over what it means for an extension to be Galois. We will look at Galois and non-Galois extensions with examples. Further, we will discuss the Kronecker-Weber Theorem, which states that every finite abelian extension of \(\mathbb\) is contained in a cyclotomic field. Time permitting, we will see what happens when we look at \(\mathbb\) adjoin the division points of a curve as a field extension of \(\mathbb\).

Join us in the Logic Colloquium for a talk by

Jonas Raab (Trinity College Dublin)

“Modal QUARC and Barcan”

I develop a modal extension of the Quantified Argument Calculus (QUARC)—a novel logical system introduced by Hanoch Ben-Yami. QUARC is meant to better capture the logic of natural language. The purpose of this paper is to develop a variable domain semantics for modal QUARC (M-QUARC), and to show that even if the usual restrictions are imposed on models with variable domains, M-QUARC-analogues of the Barcan and Converse Barcan formulas still are not validated. I introduce new restrictions—restrictions on the extension of the predicates—and show that with these in place, the Barcan and Converse Barcan formulas are valid. The upshot is that M-QUARC sheds light on the in-/validity of such formulas.

https://logic.uconn.edu/calendar/

Abstract: Underreporting losses is a prevalent behavior in insurance that is well supported by the empirical study. The goal of this talk is, however, to propose a theoretical model to explain such a behavior. To achieve this, we take an optimization perspective and consider an optimal control problem in which the insured decides whether she should report a (covered) loss. This talk will be based on the following two papers:

1. Jingyi Cao, Dongchen Li, Virginia R. Young, and Bin Zou (2023). Equilibrium reporting strategy: Two rate classes and full insurance. Journal of Risk and Insurance, https://onlinelibrary.wiley.com/doi/10.1111/jori.12451.
2. Jingyi Cao, Dongchen Li, Virginia R. Young, and Bin Zou (2024). Strategic underreporting and optimal deductible insurance. ASTIN Bulletin, https://www.researchgate.net/publication/379300509_Strategic_Underreporting_and_Optimal_Deductible_Insurance. 

This is a joint event with the UConn Control and Optimization Seminar.

Abstract. We propose efficient and reliable simulation schemes for pricing options under the stochastic-alpha-beta-rho (SABR) model. The standard two-step simulation procedures involve (i) simulation of the integrated variance conditional on terminal variance and (ii) simulation of the terminal forward price conditional on terminal variance and integrated variance. Most simulation schemes rely on the Islah approximation formula of the conditional distribution of the terminal asset price, which is seen to fail the martingale condition in general. We embed three enhanced features in our proposed simulation schemes. Firstly, we approximate the terminal forward price as the constant elasticity of variance (CEV) process that satisfies the martingale condition, an important property that precludes arbitrage. Secondly, we adopt the displaced Poisson-mixture Gamma distribution for the exact simulation of the underlying CEV process in the simulation of the terminal forward price conditional on integrated variance and terminal variance. Thirdly, we use the shifted lognormal approximation of the integrated variance to compute the integrated variance. Our enhanced procedures avoid the tedious Laplace inversion algorithm in integrated variance calculations and non-efficient inverse transform in the forward price calculations in earlier simulation schemes. Numerical results demonstrate our simulation schemes to be highly efficient, accurate, and reliable.

Speaker’s short bio: Dr. Choi is an associate professor with tenure at Peking University HSBC Business School in Shenzhen, China. He obtained his PhD in applied mathematics from Massachusetts Institute of Technology in 2005 and BS in mathematics from the Korean Advanced Institute of Science Technology in 2000. After his PhD, he worked in the industry as a quant for several years in BNP Paribas and Goldman Sachs. His research interests include quantitative finance, mathematical modeling, numerical methods, and data science. Please visit his website https://english.phbs.pku.edu.cn/2016/fulltime_0826/81.html for more information.