scholarly journals An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model

2017 ◽  
Author(s):  
Takashi Kato
Keyword(s):  
Optimal Execution ◽  
Optimal Execution Problem

scholarly journals Optimal Execution considering Trading Signal and Execution Risk Simultaneously

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yuan Cheng ◽  
Lan Wu
Keyword(s):  
Kernel Function ◽  
Price Impact ◽  
Value Functions ◽  
Feedback Form ◽  
Bellman Equations ◽  
Impact Function ◽  
Optimal Execution ◽  
Dirac Function ◽  
Hamilton Jacobi Bellman ◽  
Optimal Execution Problem

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

scholarly journals Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750020 ◽  
Author(s):  
Brian Bulthuis ◽  
Julio Concha ◽  
Tim Leung ◽  
Brian Ward
Keyword(s):  
Model Parameters ◽  
Value Functions ◽  
Continuous Time Model ◽  
Time Model ◽  
Limit Orders ◽  
Price Impacts ◽  
Dynamic Strategy ◽  
Optimal Execution ◽  
Optimal Dynamic ◽  
Optimal Execution Problem

We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trade director to provide better control on the trading rates. We formulate a stochastic control problem to determine the optimal dynamic strategy for trade execution, with a quadratic terminal penalty to ensure complete liquidation. In addition, we identify conditions on the model parameters to ensure optimality of the controls and finiteness of the associated value functions. For comparison, we also solve the schedule-following optimal execution problem that penalizes deviations from an order schedule. Numerical results are provided to illustrate the optimal market and limit orders over time.

Optimal Execution with Transient Impact

2017 ◽  
Vol 03 (01) ◽  
pp. 1750008
Author(s):  
Ngoc-Minh Dang
Keyword(s):  
Integral Equation ◽  
Calculus Of Variations ◽  
Fredholm Integral Equation ◽  
Optimal Strategy ◽  
Classical Result ◽  
No Arbitrage ◽  
Execution Costs ◽  
Optimal Execution ◽  
Optimal Execution Problem ◽  
Mean Variance

We solve the optimal execution problem including transient market impact as proposed in Gatheral (2010), and minimize execution costs with a mean-variance functional. Using a non-classical result on calculus of variations, we obtain an integral equation characterizing the optimal strategy. It takes the form of a Fredholm integral equation of the second kind. We then provide a scheme to solve it numerically and verify indeed some no-arbitrage conditions.

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