Optimal Execution for Uncertain Market Impact: Derivation and Characterization of a Continuous-Time Value Function
AbstractIn this paper, we study an optimal execution problem in the case of uncertainty in market impact to derive a more realistic market model. Our model is a generalized version of that in Kato(2009), where a model of optimal execution with deterministic market impact was formulated. 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 an optimal control problem with a L\'evy process and investigate some of its properties, which are mathematical generalizations of the results in Kato(2009). We also consider a typical example of the execution problem for a risk-neutral trader under log-linear/quadratic market impact with Gamma-distributed noise.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1301.6485.
Date of creation: Jan 2013
Date of revision: Feb 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-02-03 (All new papers)
- NEP-MST-2013-02-03 (Market Microstructure)
- NEP-UPT-2013-02-03 (Utility Models & Prospect Theory)
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- Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
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