This work studies the constrained optimal execution problem with a random market depth in the limit order *** from the real trading activities,our execution model considers the execution bounds and allows the random m...
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This work studies the constrained optimal execution problem with a random market depth in the limit order *** from the real trading activities,our execution model considers the execution bounds and allows the random market depth to be statistically correlated in different ***,it is difficult to achieve the analytical solution for this class of constrained dynamic decision *** to the special structure of this model,by applying the proposed state separation theorem and dynamic programming,we successfully obtain the analytical execution *** revealed policy is of feedback *** are provided to illustrate our solution *** results demonstrate the advantages of our model comparing with the classical execution policy.
In this study, we introduce an explicit trading-volume process into the Almgren-Chriss model, which is a standard model for optimalexecution. We propose a penalization method for deriving a verification theorem for a...
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In this study, we introduce an explicit trading-volume process into the Almgren-Chriss model, which is a standard model for optimalexecution. We propose a penalization method for deriving a verification theorem for an adaptive optimization problem. We also discuss the optimality of the volume-weighted average-price strategy of a risk-neutral trader. Moreover, we derive a second-order asymptotic expansion of the optimal strategy and verify its accuracy numerically.
Partially observed major minor LQG mean field game theory is applied to an optimal execution problem in finance; following standard financial models, controlled linear system dynamics are postulated where an instituti...
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Partially observed major minor LQG mean field game theory is applied to an optimal execution problem in finance;following standard financial models, controlled linear system dynamics are postulated where an institutio...
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Partially observed major minor LQG mean field game theory is applied to an optimal execution problem in finance;following standard financial models, controlled linear system dynamics are postulated where an institutional investor (interpreted as a major agent) in the market aims to liquidate a specific amount of shares and has partial observations of its own state (which includes its inventory). Furthermore, the market is assumed to have two populations of high frequency traders (interpreted as minor agents) who wish to liquidate or acquire a certain number of shares within a specific time, and each one of them has partial observations of its own state and the major agent's state (which include the corresponding inventories). The objective for each agent is to maximize its own wealth and to avoid the occurrence of large execution prices, large rates of trading and large trading accelerations which are appropriately weighted in the agent's performance function. The existence of-Nash equilibria together with the individual agents' trading strategies yielding the equilibria, were established. A simulation example is provided. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
We 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...
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We 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 max-imise a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic con-trol 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 optimalexecution rule are expressed in terms of the solution to a truly two-dimensional optimal stopping problem, whose asso-ciated belief-dependent free boundary b triggers the investor's optimal selling rule. The curve 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.
We study the optimal execution problem with multiplicative price impact in algorithmic trading, when an agent holds an initial position of shares of a financial asset. The interselling decision times are modeled by th...
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We study the optimal execution problem with multiplicative price impact in algorithmic trading, when an agent holds an initial position of shares of a financial asset. The interselling decision times are modeled by the arrival times of a Poisson process. The criterion to be optimized consists in maximizing the expected net present value of the gains of the agent, and it is proved that an optimal strategy has a barrier form, depending only on the number of shares left and the level of the asset price.
We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and ...
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We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, m*, and optimal placement of limit order, y*, under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points.
In this paper, we study the optimal placement of market orders in a limit order book (LOB) market when the market resilience rate, which is the rate at which market replenishes itself after each trade, is stochastic. ...
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In this paper, we study the optimal placement of market orders in a limit order book (LOB) market when the market resilience rate, which is the rate at which market replenishes itself after each trade, is stochastic. More specifically, we establish a tractable extension to the optimalexecution model in Obizhaeva and Wang (2013) by modelling the dynamics of the resilience rate to be driven by a Markov chain. When the LOB replenishes itself stochastically through time, the optimalexecution strategy becomes state-dependent, and is driven linearly by the current remaining position and the current temporary price impact, with their linear dependence based on the expectation of the dynamics of future resilience rate. A trader would optimally place more aggressive (respectively, conservative) market orders when the limit order book switches from a low to a high resilience state, (respectively, from a high to a low resilience state). Our cost saving analysis indicates that the incremental execution costs can be substantial when the agent ignores the stochastic dynamics of the market resilience rate by adopting the state-independent strategies. (C) 2019 Elsevier B.V. All rights reserved.
We consider the so-called optimal execution problem in algorithmic trading, which is the problem faced by an investor who has a large number of stock shares to sell over a given time horizon and whose actions have an ...
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We consider the so-called optimal execution problem in algorithmic trading, which is the problem faced by an investor who has a large number of stock shares to sell over a given time horizon and whose actions have an impact on the stock price. In particular, we develop and study a price model that presents the stochastic dynamics of a geometric Brownian motion and incorporates a log-linear effect of the investor's transactions. We then formulate the optimal execution problem as a degenerate singular stochastic control problem. Using both analytic and probabilistic techniques, we establish simple conditions for the market to allow for no arbitrage or price manipulation and develop a detailed characterization of the value function and the optimal strategy. In particular, we derive an explicit solution to the problem if the time horizon is infinite.
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