  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.
