Abstract: We look at the optimal execution problem from two different perspectives. First, we argue for the presence of a Brownian component in the inventory and wealth processes of individual traders. We extend the theoretical analysis of the optimal execution problem to include this result and compare the solution to the optimal behavior of a trader. Second, we provide a solution to the stochastic optimization problem using an explainable neural network optimizer, able to learn from intraday seasonality and adapt to risk preferences.

Bio: Laura Leal has completed her PhD in the Operations Research and Financial Engineering department at Princeton University. Her research interests are centered in high-frequency finance, using machine learning, deep neural networks, optimization, statistical and econometric methods to study high-frequency trading data. The main topics she has worked on include optimal execution, market making, identification of institutional activity, and tail risk.

Related papers: https://arxiv.org/abs/2104.14615 and https://arxiv.org/abs/2006.09611

Abstract: Introduced in the late 90s, the Passport Option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem that for $d>1$ risky assets remain an open problem. Even in a correlated Black-Scholes market with $d=2$ risky assets, no optimal trading strategy has been derived in closed form. Inspired by the success of deep reinforcement learning in, e.g., board games, we introduce several machine learning-powered approaches to pricing options on a portfolio value in general markets. These approaches, which prove to be successful in the one-dimensional Black-Scholes market, give valuable insights on multivariate analytic solutions.

Joint work with Josef Teichmann.

Bio: Hanna is a Ph.D. student advised by Prof. Josef Teichmann in the Stochastic Finance Group of ETH Zurich and affiliated with ETH AI Center. She is working on the mathematical theory of deep learning algorithms and their applications to Mathematical Finance.

Hanna received a B.Sc. (2015) and an M.Sc. (2018) in Applied Mathematics from the Technical University of Vienna (specializing in Financial and Actuarial Mathematics). Additionally, she received an M.Sc. (2018) in Quantitative Finance from the Vienna University of Economics and Business. Besides her studies, Hanna worked in the Advanced Analytics team of Raiffeisen Bank International in Vienna.

In her spare time, Hanna likes to play tennis, travel and enjoy a cup of coffee.

Meeting Recording: https://ucsb.zoom.us/rec/share/RUoGpFRRRs-3EQRnU00uiX7e3_N8DfsQOX3tGkB0qCgtrJwarB4sUlJfWZGnILHK.CzCAsqW6a9LoV_Cx

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