タイトル：An Optimal Execution Problem with Uncertain Market Impact (加藤恭氏との共同研究)
【abstract】 We study an optimal execution problem in the case of uncertainty in market impact to derive a more realistic market model.
First, we construct a discrete-time model as a value function of an optimal execution problem. We express the market impact function as a product of
a deterministic part (an increasing function with respect to the trader’s execution volume) and a noise part (a positive random variable).
Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control problem with a Levy process.
We also show that noise in market impact makes a risk-neutral trader underestimate the impact cost. We also study typical examples under log-linear/quadratic market impact function with Gamma-distributed noise.