An industry energy price impact model: The case of the hotel industry

1983 ◽  
Vol 15 (6) ◽  
pp. 705-714 ◽  
Author(s):  
Avner Arbel ◽  
S. Abraham Ravid
Keyword(s):  
Hotel Industry ◽  
Price Impact ◽  
Energy Price ◽  
Impact Model

scholarly journals OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT

2019 ◽  
Vol 22 (02) ◽  
pp. 1850059 ◽  
Author(s):  
WESTON BARGER ◽  
MATTHEW LORIG
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Price Impact ◽  
Trading Strategies ◽  
Impact Model ◽  
Optimal Liquidation ◽  
Special Cases ◽  
Time Price ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

scholarly journals A system of quadratic BSDEs arising in a price impact model

2016 ◽  
Vol 26 (2) ◽  
pp. 794-817 ◽  
Author(s):  
Dmitry Kramkov ◽  
Sergio Pulido
Keyword(s):  
Price Impact ◽  
Impact Model

scholarly journals Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self-Exciting Model with Decay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jiangming Ma ◽  
Xiankang Luo
Keyword(s):  
Control Method ◽  
Variable Coefficients ◽  
Price Impact ◽  
The Self ◽  
Impact Model ◽  
Nonlinear Odes ◽  
Optimal Liquidation ◽  
Optimal Control Method ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

When the market environment changes, we extend the self-exciting price impact model and further analysis of investors’ liquidation behaviour. It is assumed that the model is accompanied by an exponential decay factor when the temporary impact and its coefficient are linear and nonlinear. Using the optimal control method, we obtain that the optimal liquidation behaviours satisfy the second-order nonlinear ODEs with variable coefficients in the case of linear and nonlinear temporary impact. Next, we solve the ODEs and get the form of the investors’ optimal liquidation behaviour in four cases. Furthermore, we prove the decreasing properties of the optimal liquidation behaviour under the linear temporary impact. Through numerical simulation, we further explain the influence of the changed parameters ρ , a , b , x , and α on the investors’ liquidation strategy X t in twelve scenarios. Some interesting properties have been found.

scholarly journals An FBSDE approach to market impact games with stochastic parameters

2021 ◽  
Vol 6 (3) ◽  
pp. 237
Author(s):  
Samuel Drapeau ◽  
Peng Luo ◽  
Alexander Schied ◽  
Dewen Xiong
Keyword(s):  
Nash Equilibrium ◽  
Unique Solution ◽  
Coupled System ◽  
Price Impact ◽  
Risk Averse ◽  
Impact Model ◽  
Market Impact ◽  
Stochastic Parameters ◽  
Unique Nash Equilibrium ◽  
Fully Coupled

<p style='text-indent:20px;'>In this study, we have analyzed a market impact game between <i>n</i> risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium. </p>

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.

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