Results 1  10
of
11
Optimal Portfolio Liquidation with Limit Orders
, 2011
"... This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidityconsuming orders like Obizhaeva and Wang in [31], we link the optimal tradeschedule to the pric ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
(Show Context)
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidityconsuming orders like Obizhaeva and Wang in [31], we link the optimal tradeschedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained here solve simultaneously the two problems. As in a previous paper that solved the “intraday market making problem ” [19], the interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive “fair price” and a HamiltonJacobiBellman equation is used to solve the tradeoff between execution risk and price risk. Backtests are finally carried out to exemplify the use of our results.
A Class of Optimal Portfolio Liquidation Problems with a Linear Decreasing Impact
"... A problem of an optimal liquidation is investigated by using the AlmgrenChriss market impact model on the background that the agents liquidate assets completely. The impact of market is divided into three components: unaffected price process, permanent impact, and temporary impact. The key element ..."
Abstract
 Add to MetaCart
(Show Context)
A problem of an optimal liquidation is investigated by using the AlmgrenChriss market impact model on the background that the agents liquidate assets completely. The impact of market is divided into three components: unaffected price process, permanent impact, and temporary impact. The key element is that the variable temporary market impact is analyzed. When the temporary market impact is decreasing linearly, the optimal problem is described by a Nash equilibrium in finite time horizon. The stochastic component of the price process is eliminated from the meanvariance. Mathematically, the Nash equilibrium is considered as the secondorder linear differential equation with variable coefficients. We prove the existence and uniqueness of solutions for the differential equation with two boundaries and find the closedform solutions in special situations. The numerical examples and properties of the solution are given. The corresponding finance phenomenon is interpreted.
Dynamic Portfolio Execution
"... Abstract We analyze the optimal execution problem of a portfolio manager trading multiple assets. In addition to the liquidity and risk of each individual asset, we consider crossasset interactions in these two dimensions, which substantially enriches the nature of the problem. Focusing on the mar ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract We analyze the optimal execution problem of a portfolio manager trading multiple assets. In addition to the liquidity and risk of each individual asset, we consider crossasset interactions in these two dimensions, which substantially enriches the nature of the problem. Focusing on the market microstructure, we develop a tractable order book model to capture liquidity supply/demand dynamics in a multiasset setting, which allows us to formulate and solve the optimal portfolio execution problem. We find that crossasset risk and liquidity considerations are of critical importance in constructing the optimal execution policy. We show that even when the goal is to trade a single asset, its optimal execution may involve transitory trades in other assets. In general, optimally managing the risk of the portfolio during the execution process affects the time synchronization of trading in different assets. Moreover, links in the liquidity across assets lead to complex patterns in the optimal execution policy. In particular, we highlight cases where aggregate costs can be reduced by temporarily overshooting one's target portfolio. * Tsoukalas (gtsouk@wharton.upenn.edu) is from the Wharton School, University of Pennsylvania. Wang (wangj@mit.edu) is from MIT Sloan School of Management, CAFR and NBER. Giesecke (giesecke@stanford.edu) is from Stanford University, MS&E. We are grateful to seminar participants from