Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, December 12, 2017.

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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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Tuesday, December 12, 2017

11:00 am in 345 Altgeld Hall,Tuesday, December 12, 2017

#### The Dold--Thom theorem via factorization homology

###### Lauren Bandklayder (Northwestern University)

Abstract: The Dold--Thom theorem is a classical result in algebraic topology giving isomorphisms between the homology groups of a space and the homotopy groups of its infinite symmetric product. The goal of this talk is to outline a new proof of this theorem, which is direct and geometric in nature. The heart of this proof is a hypercover argument which identifies the infinite symmetric product as an instance of factorization homology.

1:00 pm in 345 Altgeld Hall,Tuesday, December 12, 2017

#### When does the union of two model complete theories have a model companion

###### Erik Walsberg (UIUC Math)

Abstract: Suppose $T_1,T_2$ are consistent model complete theories in languages $L_1,L_2$. Suppose that $T_1 \cap T_2$ is a complete consistent $(L_1 \cap L_2)$-theory. Then the Robinson joint consistency theorem implies $T_1 \cup T_2$ is consistent. We describe general conditions which ensure that $T_1 \cup T_2$ has a model companion. These conditions cover a number of important examples of model complete theories. Joint with Minh Tran.

3:00 pm in 345 Altgeld Hall,Tuesday, December 12, 2017

#### Affordable and Adequate Annuities with Stable Payouts: Fantasy or Reality?

###### Servaas Van Bilsen (University of Amsterdam, Netherlands)

Abstract: This paper introduces a class of investment-linked annuities that extends existing annuities by allowing portfolio shocks to be gradually absorbed into the annuity payouts. Consequently, our new class enables insurers to offer an affordable and adequate annuity with a stable payout stream. We show how to price and adequately hedge the annuity payouts in a general financial environment. In particular, our model accounts for various stylized facts of stock returns such as asymmetry and heavy-tailedness. Furthermore, the generality of our framework makes it possible to explore the impact of a parameter misspecification on the annuity price and the hedging performance.

4:00 pm in 245 Altgeld Hall,Tuesday, December 12, 2017

#### Weighted Insurance Pricing Model: Gini Shortfall, economic pricing and capital adequacy

###### Edward Furman (York University)

Abstract: The Capital Asset Pricing Model (CAPM) fetched the Nobel Prize in Economics to Professor William Sharpe back in 1990. Speaking briefly, the CAPM offers a very simple expression to price an asset in a portfolio of assets, and the just-mentioned expression is magically free of the preferences of the involved investors. As the preferences are generally unobserved in reality, and due to the appealing simplicity of the end-result, the CAPM has become one of the most influential pricing models in finance today. In this talk, among other things, I will discuss the reasons for the CAPM's low penetration into the theory of actuarial pricing, and I will then offer an insurance variant of the model. I will show how a fairly general initial set-up can yield—akin to the Sharpe's CAPM case—simple pricing expressions for a large class of risks that are symmetric or non-symmetric, light-tailed or heavy-tailed, independent or dependent. This talk hinges on a number of joint works with Professors Alexey Kuznetsov (York), Ruodu Wang (Waterloo) and Ricardas Zitikis (Western).