Discrete–Time Optimal Execution Under a Generalized Price Impact Model With Markovian Exogenous Orders

2020 ◽  
Author(s):  
Masaaki Fukasawa ◽  
Masamitsu Ohnishi ◽  
Makoto Shimoshimizu
Keyword(s):  
Discrete Time ◽  
Price Impact ◽  
Impact Model ◽  
Optimal Execution ◽  
Time Optimal

DISCRETE-TIME OPTIMAL EXECUTION UNDER A GENERALIZED PRICE IMPACT MODEL WITH MARKOVIAN EXOGENOUS ORDERS

2021 ◽  
pp. 2150025
Author(s):  
MASAAKI FUKASAWA ◽  
MASAMITSU OHNISHI ◽  
MAKOTO SHIMOSHIMIZU
Keyword(s):  
Discrete Time ◽  
Absolute Risk ◽  
Price Impact ◽  
Affine Function ◽  
Impact Model ◽  
State Variables ◽  
Optimal Execution ◽  
Execution Strategy ◽  
Time Optimal ◽  
Small Traders

This paper examines a discrete-time optimal execution problem with generalized price impact. Our main objective is to investigate the effect of price impact caused by aggregate random trade orders posed by small traders on the optimal execution strategy when orders of the small traders have a Markovian dependence. Our problem is formulated as a Markov decision process with state variables which include the last small traders’ aggregate orders. Over a finite horizon, a large trader with Constant Absolute Risk Aversion (CARA) von Neumann–Morgenstern (vN-M) utility function maximizes the expected utility from the final wealth. By applying the backward induction method of dynamic programming, we characterize the optimal execution strategy and optimal value function and conclude that the optimal execution strategy is a time-dependent affine function of three state variables. Moreover, numerical analysis prevails that the optimal execution strategy admits a “statistical arbitrage” via a round-trip trading, although our model considers a linear permanent price impact. The result differs from the previous prevailing one that a linear permanent price impact model precludes any price manipulation or arbitrage. Thus, considering a price impact caused by small traders’ orders with a Markovian dependence is significant.

Solution of Finite-Time LQP Optimal Control Problems for Discrete-Time Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 151-157 ◽  
Author(s):  
M. J. Grimble ◽  
J. Fotakis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Time Optimal Control ◽  
Infinite Time ◽  
Time Problem ◽  
Z Domain ◽  
Time Optimal ◽  
Time Optimal Control Problem

The deterministic discrete-time optimal control problem for a finite optimization interval is considered. A solution is obtained in the z-domain by embedding the problem within a equivalent infinite time problem. The optimal controller is time-invariant and may be easily implemented. The controller is related to the solution of the usual infinite time optimal control problem due to Wiener. This new controller should be of value in self-tuning control laws where a finite interval controller is particularly important.

Sign in / Sign up

Export Citation Format

Share Document