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Seminar Calendar
for events the day of Monday, November 2, 2015.

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Monday, November 2, 2015

The Marginal Cost of Risk and Capital Allocation in a Multi-Period Model

Daniel Bauer (Georgia State University)

Abstract: Capital allocation is used widely within the financial industry for purposes of pricing and performance measurement. In this paper, we consider the theoretical impact of extending the canonical model of a profit maximizing insurer beyond a single period and, in particular, consider the effect of having opportunities to raise external financing in future periods. We show that in this setting, outside of special cases, capital allocation as currently conceived cannot be done in a way to produce prices consistent with marginal cost. We go on to evaluate economically correct capital allocations based on the model in the context of an international catastrophe reinsurer with four lines of business. We find that traditional techniques can be resurrected with 1) an appropriate definition of capital, 2) a broader conception of the cost of underwriting, and 3) an appropriate risk measure connected to the fundamentals of the underlying business.

This seminar series is jointly sponsored by the Departments of Mathematics, Finance, Industrial Enterprise and Systems Engineering.

4:00 pm in 245 Altgeld Hall,Monday, November 2, 2015

Groupoids: symmetry beyond groups

Rui Fernandes (Department of Mathematics, University of Illinois)

Abstract: The notion of symmetry (of a dynamical system, of some geometry, of some algebraic system, etc.) is often taken as synonym of a group acting. In modern day mathematics, after the works of Charles Ehresmann and Alexander Grothendieck, we have come to realize that groupoids also play a fundamental role in describing symmetry. In this lecture I will discuss these ideas and how my research relates to them.

4:00 pm in 145 Altgeld Hall,Monday, November 2, 2015

Rational Surfaces from an Algebraic perspective

Eliana Duarte (UIUC Math)

Abstract: It is common practice in Algebraic Geometry to study objects such as curves and surfaces by embedding them into some projective space. In this talk the objects of study are the blow-up of $\mathbb{P}^2$ and $\mathbb{P}^1\times\mathbb{P}^1$ at a generic set of points. I will explain how to obtain an embedding of the blow-up of $\mathbb{P}^2$ by using linear systems of hypersurfaces in $\mathbb{P}^2$ which vanish at the set of generic points. Using this embedding I will use commutative algebra to obtain the defining equations of the blow up of $\mathbb{P}^2$ at a generic set of points. The goal is to try to do the same process for blow-ups of generic sets of points in $\mathbb{P}^1\times\mathbb{P}^1$.

4:00 pm in 141 Altgeld Hall,Monday, November 2, 2015

Forcing and Baire category: an introduction (Part VI, last)

Anton Bernshteyn (UIUC Math)

Abstract: In the last talk of this series we will see how the techniques of forcing are applied to derive properties of $M[G]$ (for instance, to show that $M[G]$ is a model of ZFC). In particular, we will give an overview of the proof that the Continuum Hypothesis is independent of ZFC.

5:00 pm in 241 Altgeld Hall,Monday, November 2, 2015

Continued Fractions and Operator Algebras

Florin Boca (UIUC Math)