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Probability and Computational Finance Seminar
Kevin Ou
Carnegie Mellon University
Title: Transient linear price impact and Fredholm integral equations

Abstract: I will present the paper of the same title by Gatheral, Schied, and Slynko, which unifies a large class of linear market impact models in both continuous and discrete time under a single framework. This framework translates minimization of expected implementation shortfalls to minimization of a quadratic functional of signed measures on the half real line. Thus, studying absence of price manipulations and existence and uniqueness of optimal trading strategies becomes examining positive-definiteness and regularity of quadratic functionals. In particular, optimal trading strategies are characterized by solutions to linear Fredholm integral equations, which always exists uniquely assuming a convex decreasing decay kernel specifying the exogenous market impact, a rather reasonable yet general condition. The same assumption also guarantees extra desired qualitative properties of the optima. Fourier transform is the major technical workhorse underlying these results. Time permitting, I will discuss numerical implementations or similar non-linear models.

Date: Monday, November 27, 2017
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Steve Shreve