Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Bismuth, Alexis; Guéant, Olivier; Pu, Jiang

doi:10.1007/s11579-019-00241-1

Cited by 22 publications

(23 citation statements)

References 45 publications

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“…In their model, prices contain an unpredictable martingale component, and an independent stationary (visible) predictable component-the alpha component. Bismuth, Guéant and Pu (2016) study models in which the drift of the asset price process is a latent random variable in an optimal portfolio selection setting, for an investor who seeks to maximize a Constant Absolute Risk Aversion (CARA) and Constant Relative Risk Aversion (CRRA) objective function, as well as in the cases of optimal liquidation in an Almgren-Chriss like setting.…”

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confidence: 99%

Trading algorithms with learning in latent alpha models

Casgrain

Jaimungal

2018

Mathematical Finance

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Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyzes how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the expectation–maximization algorithm. To illustrate the efficacy of the optimal strategy, we demonstrate its performance through simulations and compare it to strategies that ignore learning in the latent factors. We also provide calibration results for a particular model using Intel Corporation stock as an example.

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confidence: 99%

Trading algorithms with learning in latent alpha models

Casgrain

Jaimungal

2018

Mathematical Finance

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“…With the increase in α, investors will speed up the early liquidation speed and amount so as to obtain the maximum returns. From Figures 4,5,11,and 12, the change of b has the same effect on liquidation behaviour X t . When b gets larger, investors will liquidate faster so that they will reduce the risk of holding and get the maximum returns.…”

Section: Numerical Simulationmentioning

confidence: 78%

“…ey obtained the form of optimal liquidation behaviours by solving the HJB equation. Based on the Bayesian learning and dynamic programming techniques, Bismuth et al [11] researched the optimal portfolio choice, portfolio liquidation, and portfolio transition problems. rough the optimal control method, they found that the optimal behaviour is the solution of the HJB equation.…”

Section: Introductionmentioning

confidence: 99%

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

Luo

2021

Complexity

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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.

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“…We choose a CARA utility function U pxq "´expp´pxq, with p ą 0. It has been shown in [5,Corollary 1] that the optimal portfolio Figure 3. Simulation of pY t q tPr0,T s using the (continuous-time) optimal strategy (Opt), the (Q) estimated one, and the Benchmark strategy (Bench) to solve the Portfolio Liquidation problem.…”

Section: Portfolio Selectionmentioning

confidence: 99%

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

et al. 2019

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We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.

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Portfolio choice, portfolio liquidation, and portfolio transition under drift uncertainty

Cited by 22 publications

References 45 publications

Trading algorithms with learning in latent alpha models

Trading algorithms with learning in latent alpha models

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

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

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