The Department of Finance & Risk Engineering welcomes Marina Di Giacinto to present her talk on "Dynamic Optimal Execution with Inventory Cost" as part of the Brooklyn Quant Experience (BQE) Lecture Series*.
*Please note the time change. This event will begin at 5 p.m.
We consider the problem of optimal liquidation of a position in a risky security quoted in a financial market, where price evolution is risky and trades have an impact on price as well as uncertainty in filling orders. We generalize the Almgren and Chriss model by adding extra features that model the market maker's impact on the price by an Ornstein-Uhlenbeck process. During execution, market makers are assumed to mean revert their inventories to a preassigned capacity. The market is populated by a multiplicity of market makers with heterogeneous mean reversion time-scales. The stochastic control problem can be solved by dynamic programming approach. We first solve analytically the related HJB equation finding the value function. Then we apply verification techniques to obtain the optimal allocation strategy in the feedback form and to study its properties. In the limit as the spectrum of market makers' mean reversion rates approaches a gamma distribution, a volume-weighted average price execution under the resulting model generates a power-law expected execution price path. If time permits, we also discuss the extension of the problem to a trader maximizing a risk-adjusted profit and loss function.
Marina Di Giacinto received the Ph.D. degree in Applied Mathematics from Sapienza University of Rome. She is currently a tenured faculty member of the Department of Economics and Law at the University of Cassino. She holds the National Qualification for Associate Professorship since 2018. She has been visiting the Laboratoire CEREMADE at the Université Paris IX Dauphine and the Mathematics Department at Baruch College of The City University of New York. Her research interests include the deterministic and stochastic optimal control theory applied to Economics, Finance and Insurance. Her papers are published in leading peer-reviewed journals like Finance and Stochastics, European Journal of Operational Research, Journal of the Operational Research Society, and Quantitative Finance.
Attendance is free and highly encouraged. When possible, slides will be made available after the talk.
Refreshments will be served.