Department of

# Mathematics

Seminar Calendar
for Mathematics Colloquium - Special Lecture 2017-2018 events the year of Thursday, December 7, 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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Wednesday, October 4, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, October 4, 2017

#### Modular forms, physics, and topology

###### Dan Berwick-Evans (Illinois)

Abstract: Modular forms appear in a wide variety of contexts in physics and mathematics. For example, they arise in two dimensional quantum field theories as certain observables. In algebraic topology, they emerge in the study of invariants called elliptic cohomology theories. A long-standing conjecture suggests that these two appearances of modular forms are intimately related. After explaining the ingredients, I’ll describe some recent progress.

Tuesday, December 5, 2017

4:00 pm in 245 Altgeld Hall,Tuesday, December 5, 2017

#### Two Problems in Risk Management with Basis Risk

###### Jingong Zhang (University of Waterloo)

Abstract: Basis risk occurs naturally in a variety of finance and insurance applications, and introduces additional complexity to risk management. The theme of this presentation is to study risk management in the presence of basis risk under two settings: index insurance design and dynamic longevity hedge. In the first part of the talk, we study the problem of index insurance design under an expected utility maximization framework. We formally prove the existence and uniqueness of optimal contract for general utility functions, and obtain analytical expressions of the optimal indemnity function for exponential utility and quadratic utility functions. Our method is illustrated by a numerical example where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indexes. When compared to the linear-type contracts that have been advocated in the literature, the empirical results show that our proposed index-based contract is more efficient at reducing farmers’ basis risk. In the second part of the talk, from a pension plan sponsor’s perspective, we study dynamic hedging strategies for longevity risk using standardized securities in a discrete-time setting. The hedging securities are linked to a population which may differ from the underlying population of the pension plan, and thus basis risk arises. Drawing from the technique of dynamic programming, we develop a framework which allows us to obtain analytical optimal dynamic hedging strategies to achieve the minimum variance of hedging error. Extensive numerical experiments show that our hedging method significantly outperforms the standard “delta” hedging strategy which is commonly studied in the literature.

Tuesday, December 12, 2017

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).