- Mathematical Biology and Ecology Seminar
In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the insider’s information, which takes the form of a set of impossible paths, and the payoff of the derivative are time-invariant. This setup allows us to adapt recent work of Beiglboeck, Cox, and Huesmann [BCH16] to prove duality results and a monotonicity principle, which enables us to determine geometric properties of the optimal models. Moreover, we show that this setup is powerful, in that we are able to find analytic and numerical solutions to certain pricing and hedging problems. (Joint with B. Acciaio and M. Huesmann)
- Mathematical Finance Internal Seminar
This talk will introduce the notion of categorical rigidity and the automorphism class group of a category. We will proceed with calculations for several important categories, hopefully illuminating the inverse relationship between the automorphisms of a category and the extent to which the structure of its objects is determined categorically. To conclude, some discussion of what progress there is on currently open/unknown cases.
- Junior Algebra and Representation Seminar
I will present a new approach to study the RG flow in 3d N=4 gauge theories, based on an analysis of the Coulomb branch of vacua. The Coulomb branch is described as a complex algebraic variety and important information about the strongly coupled fixed points of the theory can be extracted from the study of its singularities. I will use this framework to study the fixed points of U(N) and Sp(N) gauge theories with fundamental matter, revealing some surprising scenarios at low amount of matter.
- String Theory Seminar
In this talk, I consider the problem of pricing and (statically)
hedging short-term contingent claims written on illiquid or
In a first part, I show how to find the best European payoff written
on a given set of underlying assets for hedging (under several
metrics) a given European payoff written on another set of underlying
assets -- some of them being illiquid or non-tradable. In particular,
I present new results in the case of the Expected Shortfall risk
measure. I also address the associated pricing problem by using
indifference pricing and its link with entropy.
In a second part, I consider the more classic case of hedging with a
finite set of simple payoffs/instruments and I address the associated
pricing problem. In particular, I show how entropic methods (Davis
pricing and indifference pricing à la Rouge-El Karoui) can be used in
conjunction with recent results of extreme value theory (in dimension
higher than 1) for pricing and hedging short-term out-of-the-money
options such as those involved in the definition of Daily Cliquet
- Mathematical and Computational Finance Seminar
In a recent paper Friedl, Zentner and Livingston asked when a sum of torus knots is concordant to an alternating knot. After a brief analysis of the problem in its full generality, I will describe some effective obstructions based on Floer type theories.
- Junior Topology and Group Theory Seminar
We count monic quartic polynomials with prescribed Galois group, by box height. Among other things, we obtain the order of magnitude for quartics, and show that non-quartics are dominated by reducibles. Tools include the geometry of numbers, diophantine approximation, the invariant theory of binary forms, and the determinant method. Joint with Rainer Dietmann.
- Number Theory Seminar
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of both natural processes (embryonic development, tree growth) and technological processes (dam construction, 3D printing). Despite the ubiquity of such processes, the mechanical aspects of surface growth are still not fully understood. In this talk we present a new approach to surface growth that allows one to address inelastic effects, path dependence of the growth process and the resulting geometric frustration. In particular, we show that incompatibility developed during deposition can be fine-tuned to ensure a particular behaviour of the system in physiological (or working) conditions. As an illustration, we compute an explicit deposition protocol aimed at "printing" arteries, that guarantees the attainment of desired stress distributions in physiological conditions. Another illustration is the growth starategy for explosive plants, allowing a complete release of residual elastic energy with a single cut.
- Industrial and Applied Mathematics Seminar
We analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Test calculations are presented that confirm our analysis.
- Computational Mathematics and Applications Seminar