4,189 research outputs found
An Optimal Execution Problem with S-shaped Market Impact Functions
In this study, we extend the optimal execution problem with convex market
impact function studied in Kato (2014) to the case where the market impact
function is S-shaped, that is, concave on and convex on
for some . We study the
corresponding Hamilton-Jacobi-Bellman equation and show that the optimal
execution speed under the S-shaped market impact is equal to zero or larger
than . Moreover, we provide some examples of the Black-Scholes
model. We show that the optimal strategy for a risk-neutral trader with small
shares is the time-weighted average price strategy whenever the market impact
function is S-shaped.Comment: 22 pages, 2 figures, forthcoming in "Communications on Stochastic
Analysis
Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact
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.Comment: 17 pages. Forthcoming in "Communications on Stochastic Analysis.
- β¦