Date: Tuesday, April 23, 2013
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: Robust Market Making
Abstract: An agent who wishes to make markets by posting limit buy and sell orders is faced with modelling the arrival rate and volume of marker orders which hit/lift their posted orders. No model can capture the true behaviour of the marketâs data generating process (DGP), hence, simplifying assumptions are often made. A natural question then arises: âhow can the agent account for the fact that they know their model is inaccurate?â i.e., how can uncertainty in the Knightian sense be addressed? In this talk, I formulate the question through a robust optimal control problem in which the agent is ambiguity averse to Poisson random measures. Specifically, the agent considers a reference measure (representing the simplified model) and all equivalent measures (representing candidate models) and penalizes them according to a quasi relative entropy. Surprisingly, the robust control problem can be reduced to solving a coupled non-linear system of ODEs, which in certain limiting cases can be solved exactly. The optimal postings show that the agent protects themselves from ambiguity in distinct ways depending from where the ambiguity stems. Interestingly, in some cases, the agent behaves as if they have perfect knowledge of the DGP but apply CARA utility; however, in general the ambiguity averse agent cannot be recast as a risk-averse one. Numerical experiments will illustrate several interesting economic insights into the problem.
This is joint work with Ãlvaro Cartea (University College London) and Ryan Donnelly (University of Toronto)
Speaker: Sebastian Jaimungal
Institution: University of Toronto
Event Organizer: Erhan Bayraktar erhan@umich.edu
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