A generalized multi-period mean-variance portfolio optimization with Markov switching parameters

In this paper, we deal with a generalized multi-period mean-variance portfolio selection problem with market parameters subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447-457]). We present necessary and sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period mean-variance problem, based on a set of interconnected Riccati difference equations, and on a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with Markov jumps selection problem.     

Multi-period portfolio optimization with linear control policies

This paper is concerned with multi-period sequential decision problems for financial asset allocation. A model is proposed in which periodic optimal portfolio adjustments are determined with the objective of minimizing a cumulative risk measure over the investment horizon, while satisfying portfolio diversity constraints at each period and achieving or exceeding a desired terminal expected wealth target. The proposed solution approach is based on a specific affine parameterization of the recourse policy, which allows us to obtain a sub-optimal but exact and explicit problem formulation in terms of a convex quadratic program.In contrast to the mainstream stochastic programming approach to multi-period optimization, which has the drawback of being computationally intractable, the proposed setup leads to optimization problems that can be solved efficiently with currently available convex quadratic programming solvers, enabling the user to effectively attack multi-stage decision problems with many securities and periods.     

基于PSO的考虑完整费用的证券组合优化研究

通过分析中国证券市场证券交易不可拆分、不能卖空的特点以及现存的各种交易费用,建立一个考虑完整交易费用的证券投资组合优化模型,同时给出一个应用粒子群算法(PSO)求解的实例。结果证明该证券投资组合优化模型的完整性和有效性,也表明PSO算法可以快速准确地求解证券投资组合优化问题。     

A class of multi-period semi-variance portfolio for petroleum exploration and development

Variance is substituted by semi-variance in Markowitz's portfolio selection model. For dynamic valuation on exploration and development projects, one period portfolio selection is extended to multi-period. In this article, a class of multi-period semi-variance exploration and development portfolio model is formulated originally. Besides, a hybrid genetic algorithm, which makes use of the position displacement strategy of the particle swarm optimiser as a mutation operation, is applied to solve the multi-period semi-variance model. For this class of portfolio model, numerical results show that the mode is effective and feasible.     

Multi-period portfolio selection using kernel-based control policy with dimensionality reduction

This paper studies a nonlinear control policy for multi-period investment. The nonlinear strategy we implement is categorized as a kernel method, but solving large-scale instances of the resulting optimization problem in a direct manner is computationally intractable in the literature. In order to overcome this difficulty, we employ a dimensionality reduction technique which is often used in principal component analysis. Numerical experiments show that our strategy works not only to reduce the computation time, but also to improve out-of-sample investment performance.     

Mean-variance model for portfolio optimization with background risk based on uncertainty theory

The aim of this paper is to develop a mean-variance model for portfolio optimization considering the background risk, liquidity and transaction cost based on uncertainty theory. In portfolio selection problem, returns of securities and assets liquidity are assumed as uncertain variables because of incidents or lacking of historical data, which are common in economic and social environment. We provide crisp forms of the model and a hybrid intelligent algorithm to solve it. Under a mean-variance framework, we analyze the portfolio frontier characteristic considering independently additive background risk. In addition, we discuss some effects of background risk and liquidity constraint on the portfolio selection. Finally, we demonstrate the proposed models by numerical simulations.     

A hybrid approach for portfolio construction: Combing two-stage ensemble forecasting model with portfolio optimization

Combining the stock prediction with portfolio optimization can improve the performance of the portfolio construction. In this article, we propose a novel portfolio construction approach by utilizing a two-stage ensemble model to forecast stock prices and combining the forecasting results with the portfolio optimization. To be specific, there are two phases in the approach: stock prediction and portfolio optimization. The stock prediction has two stages. In the first stage, three neural networks, that is, multilayer perceptron (MLP), gated recurrent unit (GRU), and long short-term memory (LSTM) are used to integrate the forecasting results of four individual models, that is, LSTM, GRU, deep multilayer perceptron (DMLP), and random forest (RF). In the second stage, the time-varying weight ordinary least square model (OLS) is utilized to combine the first-stage forecasting results to obtain the ultimate forecasting results, and then the stocks having a better potential return on investment are chosen. In the portfolio optimization, a diversified mean-variance with forecasting model named DMVF is proposed, in which an average predictive error term is considered to obtain excess returns, and a 2-norm cost function is introduced to diversify the portfolio. Using the historical data from the Shanghai stock exchange as the study sample, the results of the experiments indicate the DMVF model with two-stage ensemble prediction outperforms benchmarks in terms of return and return-risk characteristics.     

Sparse portfolio rebalancing model based on inverse optimization

This paper considers a sparse portfolio rebalancing problem in which rebalancing portfolios with minimum number of assets are sought. This problem is motivated by the need to understand whether the initial portfolio is worthwhile to adjust or not, inducing sparsity on the selected rebalancing portfolio to reduce transaction costs (TCs), out-of-sample performance and small changes in portfolio. We propose a sparse portfolio rebalancing model by adding an l₁ penalty item into the objective function of a general portfolio rebalancing model. In this way, the model is sparse with low TCs and can decide whether and which assets to adjust based on inverse optimization. Numerical tests on four typical data sets show that the optimal adjustment given by the proposed sparse portfolio rebalancing model has the advantage of sparsity and better out-of-sample performance than the general portfolio rebalancing model.     

Multistage portfolio optimization with stocks and options

We develop a multistage portfolio optimization model that utilizes options for mitigating market risk in a dynamic setting. Due to the key role of scenarios in the quality of investment decisions, a new scenario generation method is proposed that characterizes the dynamic behavior of asset returns. This methodology takes the dependence structure of different asset returns into account, and also considers serial correlations of each of the asset returns. Moreover, it preserves marginal distributions of asset returns. Also, it precludes arbitrage opportunities. To investigate the role of options, we implement the scenario generation method on a set of stocks selected from the New York Stock Exchange. Results show the high performance of the proposed scenario generation method. Afterwards, the generated set of scenarios is used as the uncertainty set for the multistage portfolio optimization model. Static and dynamic assessments are used for measuring the performance of options in mitigating market risks and generating additional returns. Finally, backtesting simulations are used for assessing different trading strategies of options.     

基于DCA-PSO算法的均值-VaR投资组合优化

投资组合决策面临现实证券市场中的大量数据,是一个复杂的组合优化问题,属于NP难问题,传统的算法难以有效求解。文化算法和粒子群算法是新近出现的两种仿生智能算法,将新提出的动态文化粒子群算法用于求解均值-VaR模型,用罚函数方法处理模型中的不等式约束,选取沪市和深市的十六支股票作为备选股票进行实证分析,数值结果表明该算法可以高效、合理地解决投资组合优化问题。     

求解均值-CVaR投资组合模型的改进粒子群算法

针对粒子群算法易跳过全局极值,且只能求解连续性问题的缺点,提出离散复形法局部搜索的思想,来有效提高粒子群算法在离散型问题中的搜索性能。针对粒子群算法易陷入局部极小的缺点,引入自适应粒子迁徙操作保证粒子的多样性,有效避免陷入局部收敛。对采用CVaR度量风险、构建有交易费用和限制证券比例的均值-CVaR投资组合模型进行仿真实验,实验结果验证了算法的有效性。将改进的粒子群算法应用到求解均值-CVaR模型的投资组合问题,与其他算法相比,该方法精度更高、性能更稳定。     

On the use of optimization models for portfolio selection: A review and some computational results

Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.     

基于改进蚁群算法的项目组合工期-成本优化

战略导向下的项目组合工期-成本优化是现代企业进行多项目管理所面临的重要问题之一,对企业实现资源效益最大化有着至关重要的促进作用。以战略导向下的项目组合工期-成本综合值最小化为研究对象,提出了优化组合项目中工序选择和执行次序的数学模型,在引入自适应权重法、调整信息素系数和混沌扰动变量的基础上,设计了求解该优化模型的改进蚁群算法。通过实例运算表明,改进后的蚁群算法,能够有效地提高算法全局搜索寻优能力和收敛速度,在求解战略导向下的项目组合工期-成本优化问题方面有较强的鲁棒性和实用价值。     

基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。     

基于双种群交流粒子群算法的离散投资组合模型

针对标准粒子群算法易陷入局部最优的缺陷,提出一种双种群交流的新型粒子群算法,利用速度变异成功地解决了上述问题;综合考虑了我国股票市场上的交易费用、整数手数投资、不允许买空卖空等问题,建立了符合我国股票市场的投资组合模型,并将双种群交流的离散粒子群算法应用于其求解过程中,给出最优投资组合。     

Large scale portfolio optimization with piecewise linear transaction costs

We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle the non-smoothness in the objective function by using spline approximations. The problem is first solved approximately using a primal-dual interior-point method applied to the smoothed problem. Then, we crossover to an active set method applied to the original non-smooth problem to attain a high accuracy solution. Our numerical tests show that we can solve large scale problems efficiently and accurately.     

Futures price modeling under exchange rate volatility and its multi-period semi-variance portfolio selection

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk-free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) with terminal boundary condition of the model is drawn. The general solution with parameters of the above PDE is derived. The parameters are estimated by using the weight least squares approach with historical data for special cases. For the objective of risk assessment, downside risk has impacted on the practitioner's view of risk apparently. Variance is substituted by semi-variance. Moreover, one period portfolio selection is extended to multi-period. A class of multi-period semi-variance model is formulated. A hybrid genetic algorithm, which makes use of the position displacement strategy of the particle swarm optimiser as a mutation operation, is applied to solve the multi-period semi-variance model. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, fuel futures in the Shanghai exchange market is selected to be an example.     

基于灵敏度分析的含比例型手续费的投资组合优化

研究含比例型手续费的离散时间投资组合优化问题. 基于马尔可夫决策过程模型和性能灵敏度分析方法, 推导两个不同投资策略之间的资产长期平均增值率的差分公式, 利用差分公式的结构特点, 证明了最优性方程, 并设计出可在线应用的策略迭代算法. 仿真实例验证了所提出算法的有效性.

     

一种混合搜索的粒子群算法

本文通过对粒子群算法个体极值、全局极值和种群极值的结合,提出一种混合搜索粒子群算法.用典型的非线性测试函数进行仿真,其实验数据和收敛曲线验证了该算法的有效性,具有快速收敛效果和寻优能力.     

Distributionally robust fuzzy project portfolio optimization problem with interactive returns

Effective project selection and staff assignment strategies directly impact organizational profitability. Based on critical value optimization criterion, this paper discusses how uncertainty and interaction impact the project portfolio return and staff allocation. Since the exact possibility distributions of uncertain parameters in practical project portfolio problems are often unavailable, we adopt variable parametric possibility distributions to characterize uncertain model parameters. Furthermore, this paper develops a novel parametric credibilistic optimization method for project portfolio selection problem. According to the structural characteristics of variable parametric possibility distributions, we derive the equivalent analytical expressions of credibility constraints, and turn the original credibilistic project portfolio model into its equivalent nonlinear mixed-integer programming models. To show the advantages of the proposed parametric credibilistic optimization method, some numerical experiments are conducted by setting various values of distribution parameters. The computational results support our arguments by comparing with the optimization method under fixed possibility distributions.