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SMSS Colloquium Talk - Alexander Schied

Wednesday, September 27, 2017
2:30 pm
Physics & Astronomy Building (PAB)
Room: 148

Title: Robust trading strategies, pathwise Itô calculus, and generalized Takagi functions

Speaker: Professor Alexander Schied - University of Waterloo

Abstract: In mainstream finance, the price evolution of a risky asset is usually modeled as a stochastic process on some probability space and hence is subject to model uncertainty. In a number of situations, however, model uncertainty can be overcome by constructing continuous-time strategies on a path-by-path basis, without any probabilistic assumptions on the asset price evolution. In this talk, we will first discuss several financial problems in which robust trading strategies can be constructed by means of Föllmer's pathwise Itô calculus. In this approach, asset price trajectories are modeled by functions that admit a prescribed pathwise quadratic variation. The second part of the talk deals with non-probabilistic constructions of such fractal functions, points out connections with the theory of generalized Takagi functions, and analyzes some of their geometric properties.

Bio: Professor Alexander Schied’s research is in probability theory and stochastic analysis with applications to mathematical finance and economics. Recent research topics include risk measurement and risk management, modeling and optimization in finance and economics, robustness and model uncertainty, and issues arising from market microstructure and price impact. Together with Hans Föllmer he co-authored the book Stochastic Finance: An Introduction in Discrete Time. He holds a doctoral degree in mathematics from the University of Bonn.

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