We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections to extend the model to multiple assets, general distributions, and risk-averse market makers. With risk-averse mar- ket makers, liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean re- verting. We illustrate the model by showing that implied volatilities predict stock returns when there is informed trading in stocks and options and market makers are risk averse.
Optimal transport and risk aversion i Kyle's model of informed trading
The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics
We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Various well-studied stochastic volatility models with and without self-exciting price/volatility co-jumps are obtained as special cases under different scaling regimes. We analyze the impact of external shocks on the market dynamics, especially their impact on jump cascades and show in a mathematically rigorous manner that many small external shocks may trigger endogenous jump cascades in asset returns and stock price volatility.
Junior female researchers in probability
The workshop will take place online and, if possible, as a hybrid event in Berlin.
We warmly invite those who identify as female to submit abstracts for contributed talks, and apply for financial support for travelling to Berlin in case we can have a hybrid event.
However, please be aware that being unable to travel should not restrain from submitting an abstract. There are special travel grants for female master students interested in gaining some insight into research and get in touch with researchers.
Of course everybody is very welcome to participate, but presentations and financial support are reserved for female participants.
Deadline for submission of abstracts and funding requests: June 30, 2021
Conference webpage: https://www.wias-berlin.de/workshops/JFRP21/
6th Berlin Workshop for Young Researchers in Mathematical Finance
The 6th Berlin Workshop for Young Researchers in Mathematical Finance takes place August 23-26. For more information, please visit
or contact the organizer Dirk Becherer.
Deep Order Flow Imbalance : Extracting Alpha From the Limit Order Book
In this talk I will describe how deep learning methods are being applied to forecast stock returns from high frequency order book states. I will review the literature in this area and describe a working paper where we evaluate return forecasts for several deep learning models for a large subset of symbols traded on the Nasdaq exchange. We investigate whether transformation of the order book states is necessary and we relate the performance of deep learning models for a symbol to its microstructural properties. This is joint work with Petter Kolm (NYU), Jeremy Turiel (UCL) and Antonio Briola (UCL).
Reinforcement learning for linear-convex models with jumps
We study finite-time horizon continuous-time linear-convex reinforcement learning problems in an episodic setting. In these problems, an unknown linear jump-diffusion process is controlled subject to nonsmooth convex costs. We start with the pure diffusion case with quadratic costs, and propose a least-squares algorithm which achieves a logarithmic regret bound of order O((lnM)(lnlnM)), with M being the number of learning episodes; the proof relies on the robustness of the associated Riccati differential equation and sub-exponential properties of the least-squares estimators. We then extend the least-squares algorithm to linear-convex learning problems with jumps, and establish a regret of the order O((MlnM)1/2); the analysis leverages the Lipschitz stability of the associated forward-backward stochastic differential equation and concentration properties of sub-Weibull random variables.
This is joint work with Matteo Basei, Xin Guo and Anran Hu.
Learning to reflect: data-driven stochastic optimal control strategies for diffusions and Lévy processes
Theoretical solutions to stochastic optimal control problems are well understood in many scenarios, however their practicability suffers from the assumption of known dynamics of the underlying stochastic process. This raises the challenge of developing purely data-driven strategies, which we explore for ergodic singular control problems associated to continuous diffusions and Lévy processes. In case of diffusion processes, the primary challenge consists of solving an exploration/exploitation tradeoff based on a minimax optimal estimation procedure of the optimal reflection boundaries with data collected in the exploration periods. Even though for Lévy processes such exploration/exploitation problem does not occur due to spatial homogeneity of the process, in this scenario we face the statistical challenge of estimating a generator functional of a subordinator associated to the Lévy process which a) cannot be observed directly from the data and b) is non-ergodic in time. We solve this problem by considering a space/time transformation of the process in form of its overshoots such that we can work with a spatially ergodic process that allows the construction of an unbiased estimator of the generator functional determining the optimal reflection boundary. We compare the results of our statistical procedure with those from deep learning approaches.