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.
- Pub Date:
- January 2013
- Quantitative Finance - Trading and Market Microstructure;
- Mathematics - Probability;
- Primary 91G80;
- Secondary 93E20;
- 17 pages. Forthcoming in "Communications on Stochastic Analysis."