Abstract
In this paper, we develop optimal trading strategies for the risk averse investor by minimizing the expected cost and the risk of execution. We present quadratic programming formulation that includes stochastic dominance constraints to render the preference relationship attitude of both risk neutral and risk averse investors. We also present a cutting plane approach to facilitate computational advantage in solving it. The efficacy of the algorithm is shown with the help of numerical examples.
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Notes
Considering tick-based movements at most exchanges, it is a reasonable assumption that the probability distributions of the cost variables in trade executions will almost always be finite discrete distributions.
For all simulation purposes in this paper, we have taken \(Z_k\)’s to be i.i.d. gamma random variables, with mean \(\mu _Z\) and variance \(\sigma _Z^2\).
In the reference of this paper, standard QPP approach refers to the QPP formulation, i.e. QPP without the FSD-constraints, given in (Khemchandani et al. 2012).
This cut belongs to the set \(J_{1}=1\), added to make the objective function finite.
Data downloaded from Yahoo! Finance website for the period of Mar’11–Apr’11.
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Khemchandani, R., Bhardwaj, A. & Chandra, S. Single asset optimal trading strategies with stochastic dominance constraints. Ann Oper Res 243, 211–228 (2016). https://doi.org/10.1007/s10479-014-1697-0
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DOI: https://doi.org/10.1007/s10479-014-1697-0