Apr 2022 - Mar 2023

Math-Fi seminar on 19 Jan.

2023.01.18 Wed up
  • Date: 19 Jan. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 18:00-19:30
  • Speaker: Tai-Ho Wang (Baruch College)
  • Title: Entropy regularized robust optimal order execution
  • Abstract:
Order execution, a mission that algorithmic trading departments and execution brokerage agencies embark on regularly, is cast as an entropy-regularized robust optimal control problem. During the course of executing a large order of significant amount, the agent faces with not only the risk of price impact that his own execution would incur towards the transaction price but also the liquidity and uncertainty of the market. The agent’s goal is to maximize an objective functional associated with his profit-and-loss of trading and simultaneously minimize the exeuction risk. It is documented that “a liquid market is one which is almost infinitely tight, which is not infinitely deep, and which is resilient enough so that prices eventually tend to their underlying value”. As such, we model the market’s liquidity and uncertainty by the principle of least relative entropy associated with the market volume. The problem of order execution is thus turned into a relative entropy-regularized (Bayesian) stochastic differential game. Standard argument of dynamic programming applies in this setting which yields that the value function of the differential game satisfies a “Bayesian” Hamilton-Jacobi-Isaacs (HJI) equation. Under the assumptions of linear-quadratic model with Gaussian prior, the Bayesian HJI equation reduces to a system of Riccati and linear differential equations. Further imposing constancy of the corresponding coefficients, the system of differential equations can be solved in closed form, resulting in analytical expressions for optimal strategy and trajectory as well as the posterior distribution of market volume. 
In conclusion, numerical examples, comparisons and discussions of the optimal strategy to conventional trading strategies are demonstrated.

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