Thu, 09 May 2024
16:00
L4

Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals

Owen Futter
(Mathematical Institute)
Abstract

In this seminar we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending traditional factor models, while keeping the resulting formulas lightweight, tractable and easily interpretable. Specifically, we achieve this by representing a trading strategy as a linear functional applied to the signature of a path (which we refer to as “Signature Trading” or “Sig-Trading”). This allows the modeller to efficiently encode the evolution of past time-series observations into the optimisation problem. In particular, we derive a concise formulation of the dynamic mean-variance criterion alongside an explicit solution in our setting, which naturally incorporates a drawdown control in the optimal strategy over a finite time horizon. Secondly, we draw parallels between classical portfolio stategies and Sig-Trading strategies and explain how the latter leads to a pathwise extension of the classical setting via the “Signature Efficient Frontier”. Finally, we give explicit examples when trading under an exogenous signal as well as examples for momentum and pair-trading strategies, demonstrated both on synthetic and market data. Our framework combines the best of both worlds between classical theory (whose appeal lies in clear and concise formulae) and between modern, flexible data-driven methods (usually represented by ML approaches) that can handle more realistic datasets. The advantage of the added flexibility of the latter is that one can bypass common issues such as the accumulation of heteroskedastic and asymmetric residuals during the optimisation phase. Overall, Sig-Trading combines the flexibility of data-driven methods without compromising on the clarity of the classical theory and our presented results provide a compelling toolbox that yields superior results for a large class of trading strategies.

 

This is based on works with Blanka Horvath and Magnus Wiese.

Thu, 07 Mar 2024

15:00 - 16:00
L4

Tensorially absorbing inclusions

Pawel Sarkowicz
Abstract

We introduce the notion of a tensorially absorbing inclusion of C*-algebras, i.e., when a unital inclusion absorbs a strongly self-absorbing C*-algebra. This is a strong condition that ensures certain properties of both algebras (and their intermediate subalgebras) in a very strong sense. We discuss such inclusions, their non-triviality, and how often these inclusions appear.

Thu, 06 Jun 2024
16:00
L4

TBC

Rouyi Zhang
(HU Berlin)
Further Information

Please join us for refreshments outside the lecture room from 1530.

Thu, 13 Jun 2024
16:00
L4

TBC

Dr Ivan Guo
(Monash University, Melbourne)
Further Information

Please join us for reshments outside the lecture room from 1530.

Thu, 02 May 2024
16:00
L4

TBC

Dr Anna Aksamit
(University of Sydney)
Further Information

Please join us for reshments outside the lecture room from 1530.

Thu, 25 Apr 2024
16:00
L4

TBC

Dr Lorenzo Croissant
(CEREMADE, Université Paris-Dauphine)
Further Information

Please join us for reshments outside the lecture room from 1530.

Mon, 25 Mar 2024
15:00
L4

Uhlenbeck compactness theorems and isometric immersions

Professor Siran Li
(Shanghai Jiao Tong University)
Abstract

In this short course, we survey the celebrated weak and strong compactness theorems proved by Karen Uhlenbeck in 1982. These results are fundamental to the gauge theory and have found numerous applications to geometry, topology, and theoretical physics. The proof is based on the ingenious idea of putting connections into ``Uhlenbeck--Coulomb gauge'', which enables the use of standard elliptic and/or nonlinear PDE techniques, as well as involved local-to-global patching arguments. We aim at giving detailed explanation of the proof, and we shall also discuss the relation between Uhlenbeck's compactness and the classical geometric problem of isometric immersions of submanifolds into Euclidean spaces.

Tue, 20 Feb 2024

14:00 - 15:00
L4

Hamiltonicity of expanders: optimal bounds and applications

Nemanja Draganić
(University of Oxford)
Abstract

An $n$-vertex graph $G$ is a $C$-expander if $|N(X)|\geq C|X|$ for every $X\subseteq V(G)$ with $|X|< n/2C$ and there is an edge between every two disjoint sets of at least $n/2C$ vertices.

We show that there is some constant $C>0$ for which every $C$-expander is Hamiltonian. In particular, this implies the well known conjecture of Krivelevich and Sudakov from 2003 on Hamilton cycles in $(n,d,\lambda)$-graphs. This completes a long line of research on the Hamiltonicity of sparse graphs, and has many applications.

Joint work with R. Montgomery, D. Munhá Correia, A. Pokrovskiy and B. Sudakov.

Mon, 12 Feb 2024
15:30
L4

A filtration of handlebody Teichmüller space

Ric Wade
((Oxford University))
Abstract

The handlebody group is defined to be the mapping class group of a handelbody (rel. boundary). It is a subgroup of the mapping class group of the surface of the handlebody, and maps onto the outer automorphism group of its fundamental group (the free group of rank equal to its genus). 

Recently Hainaut and Petersen described a subspace of moduli space forming an orbifold classifying space for the handlebody group, and combined this with work of Chan-Galatius-Payne to construct cohomology classes in the group. I will talk about how one can build on their ideas to define a cocompact EG for the handlebody group inside Teichmüller space. This is a manifold with boundary and comes with a filtration by labelled disk systems which we call the `RGB (red-green-blue) disk complex.' I will describe this filtration, use it to describe the boundary of the manifold, and speculate about potential applications to duality results. Based on work-in-progress with Dan Petersen.

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