Optimal execution strategies with generalized price impact in a discrete-time setting (Theory and Its Application of Mathematical Decision Making under Uncertainty and Ambiguity)

Abstract

This paper examines a discrete-time optimal trade execution problem with generalized price impacts. We extend a model recently discussed in Ohnishi and Shimoshimizu (2019), which consider price impacts of (aggregate) random trade execution orders posed by noise-traders as well as a large trader. Although Ohnishi and Shimoshimizu (2019) assume that trading volumes submitted by noise-traders are serially independent, this paper allows a Markovian dependence. Our new problem is formulated as a Markov decision process with state variables including the last noise-traders'orders. Over a finite horizon, the large trader with Constant Absolute Risk Aversion (CARA) von Neumann-Morgenstern (vN-M) utility function is assumed to maximize the expected utility from the final wealth. By applying the backward induction method of dynamic programming, we characterize the optimal value function and optimal trade execution strategy, and conclude that the trade execution strategy is a time-dependent affine function of three state variables: the remained trade execution volume of the large trader, (so-called) the residual effects of past price impacts caused by both of the large trader and other noise-traders, and the new state variable, i.e., the last trade execution orders submitted by noise-traders. This model enables us to investigate how the execution strategies and trade performances of a large trader are affected by the orders posed by noise-traders.