Oxford Mathematics Online Public Lecture in Partnership with Wadham College celebrating Roger Penrose's Nobel Prize
Spacetime Singularities - Roger Penrose, Dennis Lehmkuhl and Melvyn Bragg
Tuesday 16 February 2021
5.00-6.30pm
Dennis Lehmkuhl: From Schwarzschild’s singularity and Hadamard’s catastrophe to Penrose’s trapped surfaces
Roger Penrose: Spacetime singularities - to be or not to be?
Roger Penrose & Melvyn Bragg: In conversation
The course covers the standard material on nonlinear wave equations, including local existence, breakdown criterion, global existence for small data for semi-linear equations, and Strichartz estimate if time allows.
The course covers the standard material on nonlinear wave equations, including local existence, breakdown criterion, global existence for small data for semi-linear equations, and Strichartz estimate if time allows.
The course covers the standard material on nonlinear wave equations, including local existence, breakdown criterion, global existence for small data for semi-linear equations, and Strichartz estimate if time allows.
The course covers the standard material on nonlinear wave equations, including local existence, breakdown criterion, global existence for small data for semi-linear equations, and Strichartz estimate if time allows.
Abstract: Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e. removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimise prices' changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error.
=================================================
