Numerical Approximation for a Portfolio Optimization Problem Under Liquidity Risk and Costs

Gaïgi, M’hamed; Vath, Vathana Ly; Toumi, Salwa

doi:10.1007/s00245-015-9311-7

Cited by 8 publications

(3 citation statements)

References 10 publications

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“…The convergence of the solution of the numerical scheme towards the solution of the HJB equation, when the time-space step on a bounded grid goes to zero, can be shown using the standard monotonicity, stability, and consistency arguments. We refer to [12,13] for numerical schemes of the same form.…”

Section: The Discrete Problemmentioning

confidence: 99%

Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

2020

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In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations.

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Section: The Discrete Problemmentioning

confidence: 99%

Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

2020

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“…In particular, the capital asset pricing model was proposed which is significant for investment practice. After that, some combinatorial portfolio optimizations have been proposed (Dentcheva & Ruszczynski, 2003;Gaigi et al, 2016). It should be noted that the solution of the model is also of great importance.…”

Section: Introductionmentioning

confidence: 99%

Dynamic changes and multi-dimensional evolution of portfolio optimization

Zhou

Zhu

Chen

et al. 2021

Economic Research-Ekonomska Istraživanja

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Although there has been an increasing number of studies investigate portfolio optimization from different perspectives, few attempts could be found that focus on the development trend and hotspots of this research area. Therefore, it motivates us to comprehensively investigate the development of portfolio optimization research and give some deep insights into this knowledge domain. In this paper, some bibliometric methods are utilized to analyse the status quo and emerging trends of portfolio optimization research on various aspects such as authors, countries and journals. Besides, 'theories', 'models' and 'algorithms', especially heuristic algorithms are identified as the hotspots in the given periods. Furthermore, the evolutionary analysis tends to presents the dynamic changes of the cutting-edge concepts of this research area in the time dimension. It is found that more portfolio optimization studies were at an exploration stage from mean-variance analysis to consideration of multiple constraints. However, heuristic algorithms have become the driving force of portfolio optimization research in recent years. Multidisciplinary analyses and applications are also the main trends of portfolio optimization research. By analysing the dynamic changes and multi-dimensional evolution in recent decades, we contribute to presenting some deep insights of the portfolio optimization research directly, which assists researchers especially beginners to comprehensively learn this research field.

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“…Dynamic portfolio selection under permanent market impact has been formulated in Ly Vath, Mnif, and Pham (2007) as an impulse control problem under state constraints, where the authors characterize the value function as the unique constrained viscosity solution to the associated quasi-variational HJB inequality. This framework has been extended to numerical approximation in Gaigi, Ly Vath, Mnif, and Toumi (2016). Gârleanu and Pedersen (2013) derive a closed-form optimal portfolio policy for the mean-variance framework with quadratic transaction costs such that liquidity cost and market impact are included.…”

Section: Introductionmentioning

confidence: 99%

Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

Zhang

Langrené

Tian

et al. 2018

Quantitative Finance

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We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impacts. To do so, we improve the accuracy of the control randomization approach in the case of discrete controls, and propose a global iteration procedure to further improve the allocation estimates. We validate our numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model.We quantify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic allocation protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk-aversion level and investment horizon.The effect of liquidity on the design of dynamic multi-period portfolio selection methods (a.k.a. asset allocation, portfolio optimization or portfolio management) has drawn great attention from academics and practitioners alike. Liquidity affects portfolio allocation in two main ways: temporary liquidity cost and permanent market impact. Liquidity cost, also known as implementation shortfall, temporary market impact or transitory market impact, is the difference between the realized transaction price and the pre-transaction price. Market impact is the permanent shift in the asset price after a transaction, due to the post-transaction "resilience" of the limit order book. These liquidity effects depend on several factors, such as the nature of the exchange platform, the duration of the trade execution, the transaction volume, the asset volatility and so on. Up to now, liquidity modeling for dynamic portfolio selection has been impeded by the intractability of analytical solutions and by the limited capability of numerical methods to handle endogenous stochastic prices. The purpose of the present paper is to introduce a new simulation-and-regression method capable of handling multivariate portfolio allocation problems under general transaction costs, liquidity costs and market impacts. The original literature on dynamic portfolio selection started with simple problems without transaction costs. The seminal papers, Mossin (1968), Samuelson (1969), Merton (1969) and Merton (1971) provide closed-form solutions of optimal asset allocation strategies for long-term investors. In reality though, every transaction incurs commission fee (or brokerage cost), and several improvements have therefore been proposed to account for transaction cost. Examples of closed-form solutions are Davis and Norman (1990), Shr...

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Numerical Approximation for a Portfolio Optimization Problem Under Liquidity Risk and Costs

Cited by 8 publications

References 10 publications

Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

Dynamic changes and multi-dimensional evolution of portfolio optimization

Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

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