Please join the seminar via the link below:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m8ce95dc5ce34110b03a235b8b16a44e5
(Meeting number: 2624 755 6258 Password: UFcpAjH3u63)

Abstract: To ensure the solvency and financial health of the insurance sector, it is vital to accurately predict the outstanding liabilities of insurance companies. We aim to develop a dynamic statistical model that allows insurers to leverage granular transaction data on individual claims into the prediction of outstanding claim payments. However, the dynamic prediction of an insurer's outstanding liability is challenging due to the complex data structure. The liability cash flow from a claim is generated by multiple stochastic processes: a recurrent event process describing the timing of the cash flow, a payment process generating the sequence of payment amounts, and a settlement process terminating both the recurrence and payment processes. We propose to use a copula-based marked point process to jointly model the three processes. Specifically, a counting process is employed to specify the recurrent event of payment transactions; the time-to-settlement outcome is treated as a terminal event for the counting process; and the longitudinal payment amounts are formulated as the marks associated with the counting process. The dependencies among the three components are induced using the method of pair copula constructions. Compared with existing joint models for longitudinal and time-to-event data such as random effect models, the proposed approach enjoys the benefits of flexibility, computational efficiency, and straightforward prediction.

Speaker's short bio: Lu is an Assistant Professor in the School of Statistics at the University of Minnesota. She obtained my Ph.D. in Statistics from the University of Wisconsin-Madison in 2017.

Her research interests are in the development of statistical methodology motivated by insurance applications. Current research focuses on multivariate analysis, nonparametric estimation of copulas, and regression model diagnostics, especially with discrete and semi-continuous outcomes. Please visit her website for more information: https://luyang95.github.io/

In this talk, we discuss the notion of Mather-Jacobian multiplier ideals defined on an arbitrary variety. It was introduced by Ishii-Ein-Mustata and de Fernex-Docampo and generalizes the notion of multiplier ideals defined on normal varieties. We also discuss local syzygies of MJ-multiplier ideals, extending the work of Lazarsfeld-Lee and Lazarsfeld-Lee-Smith.
This is a joint work with B. Ulrich.

The integers have unique factorization: every integer bigger than 1 is a product of primes in only one way (up to the order of the factors). But if we go beyond the integers to other systems in which we can multiply and factor, unique factorization sometimes holds and sometimes doesn't.

In this talk we'll meet some situations where unique factorization is not true and see how the presence or failure of unique factorization is related to different areas of math. In particular, we'll meet an overlooked example from high school math where unique factorization breaks down.

Note: Free refreshments. The talk starts at 5:40.