Title: Optimal trading strategy under linear-percentage temporary impact price dynamics with conditional value-at-risk as timing risk measure
Authors: Arti Singh; Selvamuthu Dharmaraja
Addresses: Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India ' Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
Abstract: This paper attempts to solve constrained optimal trading problem of minimising expected execution cost subject to non-negativity constraints for risk neutral as well as risk averse investors. The optimal trading problems are modelled under linear-percentage temporary impact price dynamics (LPT price model) of underlying asset's execution price dynamics. The algorithm to solve optimal trading problem with non-negativity constraints under LPT price model by static approximation method (SA method) is detailed. Furthermore, a comprehensive discussion of applicability of other existing approaches in literature to solve proposed problems and, their limitations are presented to justify use of SA method for the same. In case of a risk averse investor, the conditional value-at-risk (CVaR) is taken as a measure for the timing risk. The extensive numerical illustrations on simulated data as well as on the real market data depict the practical significance of the proposed optimal trading problems.
Keywords: optimal trading; conditional value-at-risk; CVaR; dynamic programming; quadratic programming; risk averse investment; price impact; trading strategies; LPT price dynamics; linear-percentage temporary impact; timing risk; risk neutral investment; simulation.
International Journal of Decision Support Systems, 2016 Vol.2 No.1/2/3, pp.13 - 37
Received: 15 Aug 2015
Accepted: 11 Mar 2016
Published online: 23 Jan 2017 *