Department of

# Mathematics

Seminar Calendar
for events the day of Friday, January 24, 2020.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2019           January 2020          February 2020
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29



Friday, January 24, 2020

3:00 pm in 243 Altgeld Hall,Friday, January 24, 2020

#### Statistical inference for mortality models

###### Chen Ling (Georgia State University)

Abstract: Underwriters of annuity products and administrators of pension funds are under ﬁnancial obligation to their policyholder until the death of counterparty. Hence, the underwriters are subject to longevity risk when the average lifespan of the entire population increases, and yet, such risk can be managed through hedging practices based on parametric mortality models. As a benchmark mortality model in insurance industry is Lee-Carter model, we ﬁrst summarize some ﬂaws regarding the model and inference methods derived from it. Based on these understandings we propose a modiﬁed Lee-Carter model, accompanied by a rigorous statistical inference with asymptotic results and satisfactory numerical and simulation results derived from a small sample. Then we propose bias corrected estimator which is consistent and asymptotically normally distributed regardless of the mortality index being a unit root or stationary AR(1) time series. We further extend the model to accommodate AR(2) process for mortality index, and, a bivariate dataset of U.S. mortality rates. Finally, we conclude by a detailed model validation and some discussions of potential hedging practices based on our parametric model.

3:00 pm in 347 Altgeld Hall,Friday, January 24, 2020

#### Organizational Meeting

###### Kesav Krishnan (UIUC Math)

Abstract: This organizational meeting will be to decide on a schedule of speakers. All are welcome

4:00 pm in 141 Altgeld Hall,Friday, January 24, 2020

#### Organizational Meeting

###### Nachiketa Adhikari (UIUC)

Abstract: We will draft a schedule of the seminar talks this semester. Please join us and sign up if you want to speak (you don't have to decide on a topic or abstract now). As usual, there will be cookies. All are welcome!

4:00 pm in 245 Altgeld Hall,Friday, January 24, 2020

#### Logical and geometric tameness over the real line.

###### Erik Walsberg (University of California, Irvine)

Abstract: There are now a number of important and well-understood examples of logically tame first order structures over the real numbers such as the ordered field of real numbers and the ordered field of real numbers equipped with the exponential function. In these examples subsets of Euclidean space which are (first order) definable are geometrically very well behaved. Recent research had yielded general theorems in this direction. I will discuss one result in this subject: A first order structure on the real line which expands the ordered vector space of real numbers and defines a closed set X such that the topological dimension of X is strictly less then the Hausdorff dimension of X defines every bounded Borel set. Informally: An expansion of the ordered real vector space which defines a fractal is maximally wild from the viewpoint of logic. Joint with Fornasiero and Hieronymi.