May 2024 CDT Workshop

Student talks: Yifan Jiang (Oxford) and Roan Talbut (Imperial);  Speaker talk: Dr Leandro Sanchez-Betancourt (Oxford)

13:30    Yifan Jiang, University of Oxford

Sensitivity of causal distributionally robust optimization

In this talk, we study the distributionally robust optimization (DRO) in a dynamic context. We consider a general penalized DRO problem with a causal transport-type penalization. We derive the sensitivity of the causal DRO with respect to the level of the uncertainty of the model. Moreover, we investigate the case where a martingale constraint is imposed on the underlying model. As an application, this leads to a non-parametric Greek to path-dependent options. If time permits, I will also talk about passing to the continuous-time limit under two different scaling regimes.

14:10    Roan Talbut, Imperial College London     

Tropical Gradient Descent

In this talk, I will introduce tropical geometry - a variant of algebraic geometry which provides a geometric lens through which to view non-smooth optimisation problems, and that has become increasingly studied in applications such as computational biology, economics, and computer science. We will review various types of convexity which arise in tropical problems, and we propose a new gradient descent method for solving tropical optimisation problems. Theoretical results establish global solvability for tropically quasi-convex problems, while numerical experiments demonstrate the method's superior performance over classical descent for tropical optimisation problems which exhibit tropical quasi-convexity but not classical convexity. Notably, tropical gradient descent seamlessly integrates into advanced optimisation methods, such as Adam, offering improved overall performance.

14:50    Tea and coffee break

15:00    Dr Leandro Sanchez-Betancourt, University of Oxford

Brokers, Informed Traders, and Noise Traders

We study the equilibrium of the trading strategies between a broker and her clients.  The broker streams bespoke quotes to the informed trader and to a noise trader, and also trades in the lit market.  The flow of the noise trader is uninformative and the broker trades with the noise trader at a profit, on average. On the other hand, the informed trader has privileged information about the trend in the price of the asset, so the broker trades with the informed trader at a loss, on average. These losses are payment for toxic flow from which the broker tries to learn the trend signal. We demonstrate the efficacy of the trading strategy of the broker in several scenarios and perform robustness analysis against misspecification of model parameters. We employ simulations to conclude that the strategy we derived outperforms current market practices.

16:00    End of workshop

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16:00     Fridays@4 – 3-Minute Thesis Competition