Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact
Communications on Stochastic Analysis, 9(3), 343-366 (2015)
24 Pages Posted: 9 Jun 2015 Last revised: 8 Nov 2015
Date Written: March 10, 2015
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton--Jacobi--Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.
Keywords: Optimal execution, market impact, liquidity uncertainty, Levy process
Suggested Citation: Suggested Citation