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Journal articles on the topic 'Optimal liquidation portfolio'

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Published: 25 May 2024

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1

Guéant, Olivier, Charles-Albert Lehalle, and Joaquin Fernandez-Tapia. "Optimal Portfolio Liquidation with Limit Orders." SIAM Journal on Financial Mathematics 3, no. 1 (January 2012): 740–64. http://dx.doi.org/10.1137/110850475.

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2

Caccioli, Fabio, Susanne Still, Matteo Marsili, and Imre Kondor. "Optimal liquidation strategies regularize portfolio selection." European Journal of Finance 19, no. 6 (July 2013): 554–71. http://dx.doi.org/10.1080/1351847x.2011.601661.

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3

Ankirchner, Stefan, Christophette Blanchet-Scalliet, and Anne Eyraud-Loisel. "Optimal portfolio liquidation with additional information." Mathematics and Financial Economics 10, no. 1 (May 31, 2015): 1–14. http://dx.doi.org/10.1007/s11579-015-0147-3.

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4

Brown, David B., Bruce Ian Carlin, and Miguel Sousa Lobo. "Optimal Portfolio Liquidation with Distress Risk." Management Science 56, no. 11 (November 2010): 1997–2014. http://dx.doi.org/10.1287/mnsc.1100.1235.

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5

NYSTRÖM, KAJ, SIDI MOHAMED OULD ALY, and CHANGYONG ZHANG. "MARKET MAKING AND PORTFOLIO LIQUIDATION UNDER UNCERTAINTY." International Journal of Theoretical and Applied Finance 17, no. 05 (July 28, 2014): 1450034. http://dx.doi.org/10.1142/s0219024914500344.

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Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

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6

Kharroubi, Idris, and Huyên Pham. "Optimal Portfolio Liquidation with Execution Cost and Risk." SIAM Journal on Financial Mathematics 1, no. 1 (January 2010): 897–931. http://dx.doi.org/10.1137/09076372x.

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7

Guéant, Olivier, Jean-Michel Lasry, and Jiang Pu. "A Convex Duality Method for Optimal Liquidation with Participation Constraints." Market Microstructure and Liquidity 01, no. 01 (June 2015): 1550002. http://dx.doi.org/10.1142/s2382626615500021.

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In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this paper, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The method we propose is very general as it can be applied to multi-asset portfolios with any form of execution costs, including a bid-ask spread component, even when participation constraints are imposed. Our method, based on convex duality, only requires Hamiltonian functions to have C1,1 regularity while classical methods require additional regularity and cannot be applied to all cases found in practice.

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8

Schied, Alexander, and Tao Zhang. "A STATE-CONSTRAINED DIFFERENTIAL GAME ARISING IN OPTIMAL PORTFOLIO LIQUIDATION." Mathematical Finance 27, no. 3 (September 29, 2015): 779–802. http://dx.doi.org/10.1111/mafi.12108.

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9

Neuman, Eyal, and Alexander Schied. "Optimal portfolio liquidation in target zone models and catalytic superprocesses." Finance and Stochastics 20, no. 2 (October 20, 2015): 495–509. http://dx.doi.org/10.1007/s00780-015-0280-0.

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10

Yao, Dingjun, Hailiang Yang, and Rongming Wang. "OPTIMAL DIVIDEND AND REINSURANCE STRATEGIES WITH FINANCING AND LIQUIDATION VALUE." ASTIN Bulletin 46, no. 2 (January 25, 2016): 365–99. http://dx.doi.org/10.1017/10.1017/asb.2015.28.

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AbstractThis study investigates a combined optimal financing, reinsurance and dividend distribution problem for a big insurance portfolio. A manager can control the surplus by buying proportional reinsurance, paying dividends and raising money dynamically. The transaction costs and liquidation values at bankruptcy are included in the risk model. Under the objective of maximising the insurance company's value, we identify the insurer's joint optimal strategies using stochastic control methods. The results reveal that managers should consider financing if and only if the terminal value and the transaction costs are not too high, less reinsurance is bought when the surplus increases or dividends are always distributed using the barrier strategy.

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11

Ma, Jiangming, Zheng Yin, and Hongjing Chen. "A Class of Optimal Portfolio Liquidation Problems with a Linear Decreasing Impact." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3758605.

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A problem of an optimal liquidation is investigated by using the Almgren-Chriss market impact model on the background that the n 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 mean-variance. Mathematically, the Nash equilibrium is considered as the second-order linear differential equation with variable coefficients. We prove the existence and uniqueness of solutions for the differential equation with two boundaries and find the closed-form solutions in special situations. The numerical examples and properties of the solution are given. The corresponding finance phenomenon is interpreted.

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12

CHEVALIER, ETIENNE, VATHANA LY VATH, SIMONE SCOTTI, and ALEXANDRE ROCH. "OPTIMAL EXECUTION COST FOR LIQUIDATION THROUGH A LIMIT ORDER MARKET." International Journal of Theoretical and Applied Finance 19, no. 01 (February 2016): 1650004. http://dx.doi.org/10.1142/s0219024916500047.

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We study the problem of optimally liquidating a large portfolio position in a limit-order market. We allow for both limit and market orders and the optimal solution is a combination of both types of orders. Market orders deplete the order book, making future trades more expensive, whereas limit orders can be entered at more favorable prices but are not guaranteed to be filled. We model the bid-ask spread with resilience by a jump process, and the market-order arrival process as a controlled Poisson process. The objective is to minimize the execution cost of the strategy. We formulate the problem as a mixed stochastic continuous control and impulse problem for which the value function is shown to be the unique viscosity solution of the associated variational inequalities. We conclude with a calibration of the model on recent market data and a numerical implementation.

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13

Chebbi, Souhail, and Senda Ounaies. "Optimal Investment of Merton Model for Multiple Investors with Frictions." Mathematics 11, no. 13 (June 27, 2023): 2873. http://dx.doi.org/10.3390/math11132873.

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We investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover the transaction costs and liquidity models studied previously in the literature. We suppose that each investor maximizes their utility function over all controls that keep the value of the portfolio after liquidation non-negative. In the main results of this paper, we prove the existence of an optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model via constructing a truncated economy, and the optimal strategy is obtained using a classical argument of limits.

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14

Henderson, Vicky, and David Hobson. "OPTIMAL LIQUIDATION OF DERIVATIVE PORTFOLIOS." Mathematical Finance 21, no. 3 (October 19, 2010): 365–82. http://dx.doi.org/10.1111/j.1467-9965.2010.00455.x.

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15

Gibson Brandon, R., and S. Gyger. "Optimal hedge fund portfolios under liquidation risk." Quantitative Finance 11, no. 1 (January 2011): 53–67. http://dx.doi.org/10.1080/14697688.2010.506883.

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16

Schied, Alexander, and Torsten Schoeneborn. "Optimal Portfolio Liquidation for CARA Investors." SSRN Electronic Journal, 2007. http://dx.doi.org/10.2139/ssrn.1018088.

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17

Brown, David B., Bruce I. Carlin, and Miguel Sousa Lobo. "Optimal Portfolio Liquidation with Distress Risk." SSRN Electronic Journal, 2010. http://dx.doi.org/10.2139/ssrn.1570223.

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18

Fu, Guanxing, Paulwin Graewe, Ulrich Horst, and Alexandre Popier. "A Mean Field Game of Optimal Portfolio Liquidation." Mathematics of Operations Research, February 5, 2021. http://dx.doi.org/10.1287/moor.2020.1094.

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We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with a finite terminal value yet a singular driver. Extending the method of continuation to linear-quadratic FBSDEs with a singular driver, we prove that the MFG has a unique solution. Our existence and uniqueness result allows proving that the MFG with a possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.

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19

Gu, Jiawen, and Mogens Steffensen. "Optimal Portfolio Liquidation and Dynamic Mean-Variance Criterion." SSRN Electronic Journal, 2015. http://dx.doi.org/10.2139/ssrn.2687999.

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20

Li, Yi, Ju’e Guo, Kin Keung Lai, and Jinzhao Shi. "Optimal portfolio liquidation with cross-price impacts on trading." Operational Research, June 8, 2020. http://dx.doi.org/10.1007/s12351-020-00572-8.

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21

Fu, Guanxing, Ulrich Horst, and Xiaonyu Xia. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies." Mathematics of Operations Research, November 23, 2023. http://dx.doi.org/10.1287/moor.2022.0174.

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We consider a mean-field control problem with càdlàg semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and we show that it is of linear-quadratic form and that its coefficients satisfy a coupled system of nonstandard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a sequence of discrete-time models. A sophisticated transformation shows that the system can be brought into standard Riccati form, from which we deduce the existence of a global solution. Our analysis shows that the optimal strategy jumps only at the beginning and the end of the trading period. Funding: Financial support is through the National Natural Science Foundation of China [Grants 12101465 and 12101523], Hong Kong Research Grants Council (Early Career Scheme) [Grant 25215122], Hong Kong Polytechnic University [Internal Grant P0044694, Internal Grant P0045668, and Startup Grant P0035348], and the Hong Kong Research Centre for Quantitative Finance [Grant P0042708].

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22

Chen, Jingnan, Liming Feng, Jiming Peng, and Yu Zhang. "Optimal portfolio execution with a Markov chain approximation approach." IMA Journal of Management Mathematics, August 16, 2021. http://dx.doi.org/10.1093/imaman/dpab025.

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Abstract We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

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23

Voß, Moritz. "A two-player portfolio tracking game." Mathematics and Financial Economics, July 26, 2022. http://dx.doi.org/10.1007/s11579-022-00324-6.

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AbstractWe study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank et al. (Math Financial Economics 11(2):215–239 2017). Specifically, both agents track their own stochastic running trading targets while interacting through common aggregated temporary and permanent price impact à la Almgren and Chriss (J Risk 3:5–39 2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for a unique and explicitly available open-loop Nash equilibrium. Our results reveal how the equilibrium strategies of the two players take into account the other agent’s trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the relation between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement and extend existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation games.

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24

Xu, Fengmin, Xuepeng Li, Yu‐Hong Dai, and Meihua Wang. "New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact." International Transactions in Operational Research, October 12, 2022. http://dx.doi.org/10.1111/itor.13219.

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25

Huang, Yu, Nengjiu Ju, and Hao Xing. "Performance Evaluation, Managerial Hedging, and Contract Termination." Management Science, September 29, 2022. http://dx.doi.org/10.1287/mnsc.2022.4533.

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We develop a dynamic model where a principal contracts with an agent to operate a firm. The agent, protected by limited liability, trades privately a market portfolio to hedge market risk in his compensation. When liquidation cost of the firm is proportional to its size, the principal manages the termination risk by loading the contract with a positive market component, which alleviates termination risk in normal market conditions but makes termination more likely after negative market shocks. The optimal contract displays a dynamic mixture of absolute and relative performance evaluations and is implemented using a dynamic deferred compensation account. This paper was accepted by Agostino Capponi, finance.

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26

Dammann, Felix, and Giorgio Ferrari. "Optimal execution with multiplicative price impact and incomplete information on the return." Finance and Stochastics, June 29, 2023. http://dx.doi.org/10.1007/s00780-023-00508-y.

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AbstractWe study an optimal liquidation problem with multiplicative price impact in which the trend of the asset price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time horizon a fixed amount of assets in order to maximise a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic control problem featuring a finite-fuel constraint and partial observation. We provide a complete analysis of an equivalent three-dimensional degenerate problem under full information, whose state process is composed of the asset price dynamics, the amount of available assets in the portfolio, and the investor’s belief about the true value of the asset’s trend. Its value function and optimal execution rule are expressed in terms of the solution to a truly two-dimensional optimal stopping problem, whose associated belief-dependent free boundary $b$ b triggers the investor’s optimal selling rule. The curve $b$ b is uniquely determined through a nonlinear integral equation, for which we derive a numerical solution through an application of the Monte Carlo method. This allows us to understand the value of information in our model as well as the sensitivity of the problem’s solution with respect to the relevant model parameters.

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27

Henderson, Vicky, and David Hobson. "OPTIMAL LIQUIDATION OF DERIVATIVE PORTFOLIOS." Mathematical Finance, May 2011, no. http://dx.doi.org/10.1111/j.1467-9965.2011.00477.x.

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28

Hess, Markus. "Optimal Liquidation of Electricity Futures Portfolios: An Anticipative Market Impact Model." SSRN Electronic Journal, 2013. http://dx.doi.org/10.2139/ssrn.2254293.

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29

Dolinskyi, Leonid, and Yan Dolinsky. "Optimal liquidation with high risk aversion and small linear price impact." Decisions in Economics and Finance, March 13, 2024. http://dx.doi.org/10.1007/s10203-024-00435-3.

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AbstractWe consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options in the case where the investor is required to liquidate her position. Our main result is establishing a non-trivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. We compute the limit of the corresponding utility indifference prices and find explicitly a family of portfolios which are asymptotically optimal.

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