Department of

# Mathematics

Seminar Calendar
for events the day of Monday, April 19, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, April 19, 2021

1:00 pm in via Zoom,Monday, April 19, 2021

#### Metamodeling for variable annuity valuation: What works and what does not

###### Xiaochen Jing   [email] (University of Wisconsin, Madison)

Abstract: Variable Annuities have become popular retirement products with various options of guarantees, but their complex design also makes liability management a difficult task for insurers. There have been several dozen papers published in the past years on exploring the use of statistical learning and metamodeling approaches for Variable Annuity valuation and risk management in the actuarial science and quantitative finance literatures. However, they all focus on specific techniques in the context of synthetic data. In this paper, I investigate the effectiveness of metamodeling approaches with different experimental designs and metamodels with real-world Variable Annuity contracts. In particular, I use textual analysis to extract and formulate value-related features and develop a flexible and comprehensive simulation-based scheme for Variable Annuity valuation. I find that (1) real-world variable annuity contracts are very complex and the intricate relations between their valuation and features are difficult to obtain. And (2) the overall performance of a metamodeling method depends on the employed machine learning methods as well as the sample size---though not substantially on the sampling methods. Both improve performance at the cost of longer runtime.

3:00 pm in Zoom,Monday, April 19, 2021

#### Topological Modular forms with level structure

###### Abhra Kundu (UIUC)

Abstract: Goerss-Hopkins-Miller theorem gives us a way of extracting homotopic information hidden inside the Moduli Stack of Elliptic curves by constructing an ́etale presheaf of E∞-ring spectra. Evaluating the presheaf on some particular Modular curves produces TMF with level structure. This presheaf is not only defined on ́etale sites of the Moduli Stack of Elliptic curves but also on Moduli Stack of generalized Elliptic curves but unfortunately the modular curves in this case are no longer ́etale over this stack. So, the presheaf can no longer be evaluated on these modular curves. But, it turns out that by refining the topology on this stack one can define a presheaf which not only produces the universal object, Tmf , but also produces a functorial family of objects, Tmf with level structures, which are the analogs of TMF with level structures. In this talk I will state this result and try to explain this refinement. Please email vb8 at illinois dot edu for the zoom details.