Abstract
We devise an optimal allocation strategy for the execution of a predefined number of stocks in a given time frame using the technique of discrete-time Stochastic Control Theory for a defined market model. This market structure allows an instant execution of the market orders and has been analyzed based on the assumption of discretized geometric movement of the stock prices. We consider two different cost functions where the first function involves just the fiscal cost while the cost function of the second kind incorporates the risks of non-strategic constrained investments along with fiscal costs. Precisely, the strategic development of constrained execution of K stocks within a stipulated time frame of T units is established mathematically using a well-defined stochastic behaviour of stock prices and the same is compared with some of the commonly-used execution strategies using the historical stock price data.
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- 1.
As per the stock data obtained from Yahoo Finance.
- 2.
As per the stock data obtained from Yahoo Finance.
References
Almgren, R., Chriss, N.: Value under liquidation. Risk 12(12), 61–63 (1999)
Bertsimas, D., Andrew, W.Lo.: Optimal control of execution costs. J. Financ. Mark. 1(1), 1–50 (1998)
Cont, R., Kukanov, A.: Optimal order placement in limit order markets (2013)
Dimitri, P.: Bertsekas. Dynamic Programming and Stochastic Control. Academic Press, New York (1976)
Even-Dar, E., Kakade, S., Mansour, Y.: Reinforcement learning in POMDPs without resets (2005)
Land, A.H., Doig, A.G.: An automatic method of solving discrete programming problems. Econ.: J. Econ. Soc. 497–520 (1960)
Nevmyvaka, Y., Feng, Y., Kearns, M.: Reinforcement learning for optimized trade execution. In: Proceedings of the 23rd International Conference On Machine Learning, pp. 673–680. ACM (2006)
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction, vol. 1. MIT press, Cambridge (1998)
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We thank the conference participants at Statfin2017 for their insightful comments and suggestions which has helped us to improve our work.
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Bansal, A., Mukherjee, D. (2019). Optimizing Execution Cost Using Stochastic Control. In: Abergel, F., Chakrabarti, B., Chakraborti, A., Deo, N., Sharma, K. (eds) New Perspectives and Challenges in Econophysics and Sociophysics. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-030-11364-3_4
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DOI: https://doi.org/10.1007/978-3-030-11364-3_4
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