  We study an optimal execution problem with uncertain market impact to derive
a more realistic market model. We construct a discrete-time model as a value
function for optimal execution. Market impact is formulated as the product of a
deterministic part increasing with execution volume and a positive stochastic
noise part. 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.
