Mean–variance portfolio selection based on a generalized BNS stochastic volatility model

We study a mean–variance portfolio selection problem via optimal feedback control based on a generalized Barndorff-Nielsen and Shephard stochastic volatility model, where an investor trades in a generalized Black–Scholes market. The random coefficients of the market are driven by non-Gaussian Ornstein–Uhlenbeck processes that are independent of the underlying multi-dimensional Brownian motion. Our contribution is to explicitly compute and justify optimal portfolios over an admissible set that is large enough to cover some important classes of strategies such as the class of feedback controls of Markov type. Concretely, the mean–variance efficient portfolios and efficient frontiers are explicitly calculated through the method of generalized linear-quadratic control and explicitly constructed solutions to three integro-partial differential equations under a quite mild condition that only requires one stock whose appreciation-rate process is different from the interest-rate process. Related minimum variance issue is also addressed via our main results.     

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L₁ regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios.     

Growth optimal investment in discrete-time markets with proportional transaction costs

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we also solve the optimal portfolio selection problem in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations.     

市场指数模型下最优证券组合的简化算法

研究市场指数模型下最优证券组合的简化算法,扩展了针对预期超额收益—贝塔比率最大化提出的简化算法,并将其应用于确定最小风险证券组合构成、考虑风险容忍度的最优证券组合构成、允许和不允许限制性卖空情况下有效证券组合构成及其变动。     

Mean-Extended Gini Portfolios: A 3D Efficient Frontier

Using a numerical optimization technique we construct the mean-extended Gini (MEG) efficient frontier as a workable alternative to the mean-variance efficient frontier. MEG enables the introduction of specific risk aversion into portfolio selection. The resulting portfolios are stochastically dominant for all risk-averse investors. Solving for MEG portfolios allows investors to tailor portfolios for specific risk aversion. The extended Gini is calculated by the covariance of asset returns with a weighing function of the cumulative distribution function (CDF) of these returns. In a sample of asset returns, the CDF is estimated by ranking returns. In this case, analytical optimization techniques using continuous gradient approaches are unavailable, thus the need to develop numerical optimization techniques. In this paper we develop a numerical optimization algorithm that finds the portfolio optimal frontier for arbitrarily large sets of shares. The result is a 3-dimension MEG efficient frontier in the space formed by mean, the extended Gini, and the risk aversion coefficient.     

Solving a comprehensive model for multiobjective project portfolio selection

Any organization is routinely faced with the need to make decisions regarding the selection and scheduling of project portfolios from a set of candidate projects. We propose a multiobjective binary programming model that facilitates both obtaining efficient portfolios in line with the set of objectives pursued by the organization, as well as their scheduling regarding the optimum time to launch each project within the portfolio without the need for a priori information on the decision-maker's preferences. Resource constraints, the possibility of transferring resources not consumed in a given a period to the following one, and project interdependence have also been taken into account. Given that the complexity of this problem increases as the number of projects and the number of objectives increase, we solve it using a metaheuristic procedure based on Scatter Search that we call SS-PPS (Scatter Search for Project Portfolio Selection). The characteristics and effectiveness of this method are compared with other heuristic approaches (SPEA and a fully random procedure) using computational experiments on randomly generated instances.

Statement of scope and purpose

This paper describes a model to aid in the selection and scheduling of project portfolios within an organization. The model was designed assuming strong interdependence between projects, which therefore have to be assessed in groups, while allowing individual projects to start at different times depending on resource availability or any other strategic or political requirements, which involves timing issues. The simultaneous combination of project portfolio selection and scheduling under general conditions involves known drawbacks that we attempt to remedy. Finally, the model takes into account multiple objectives without requiring a priori specifications regarding the decision-maker's preferences.The resolution of the problem was approached using a metaheuristic procedure, which showed by computational experiments good performance compared with other heuristics.     

Parallel Optimization of Sparse Portfolios with AR-HMMs

In this paper we optimize mean reverting portfolios subject to cardinality constraints. First, the parameters of the corresponding Ornstein–Uhlenbeck (OU) process are estimated by auto-regressive Hidden Markov Models (AR-HMM), in order to capture the underlying characteristics of the financial time series. Portfolio optimization is then performed by maximizing the return achieved with a predefined probability instead of optimizing the predictability parameter, which provides more profitable portfolios. The selection of the optimal portfolio according to the goal function is carried out by stochastic search algorithms. The presented solutions satisfy the cardinality constraint in terms of providing a sparse portfolios which minimize the transaction costs (and, as a result, maximize the interpretability of the results). In order to use the method for high frequency trading (HFT) we utilize a massively parallel GPGPU architecture. Both the portfolio optimization and the model identification algorithms are successfully tailored to be running on GPGPU to meet the challenges of efficient software implementation and fast execution time. The performance of the new method has been extensively tested both on historical daily and intraday FOREX data and on artificially generated data series. The results demonstrate that a good average return can be achieved by the proposed trading algorithm in realistic scenarios. The speed profiling has proven that GPGPU is capable of HFT, achieving high-throughput real-time performance.     

跳跃扩散股价的最优投资组合选择

假定股票价格服从跳跃扩散过程.在传统均值-方差组合投资模型基础上,最大化最终收益的期望及最小化最终财富的方差.引进一个随机线性二次最优控制问题作为原问题的近似问题.证明了一个状态为跳跃扩散过程的一般最优控制问题的验证性定理.应用验证性定理求解HJB(Hamilton-Jacobi-Bellman)方程得到了原问题的最优策略.最后还给出了原问题有效前沿的表达式.     

基于战略对应的IT项目组合选择模型

把信息技术项目当作组合来管理可以通过平衡风险和收益来促进企业目标和IT应用的结合,但由于决策信息的不确定性和IT项目目标与企业战略的难以对应,企业面临IT项目组合选择的挑战。构建基于战略对应的IT项目组合选择模型,其中模糊集和模糊层次分析法用来刻画不确定信息和评估IT项目风险、成本及收益,关键成功因素法用来提高IT项目与企业战略的对应,并建立模糊0－1整数规划。利用定性可能性理论把模糊组合选择模型转化为一般可求解的整数规划形式,最后用一个案例说明模型的用法。     

Possibilistic mean-variance models and efficient frontiers for portfolio selection problem

In this paper, it is assumed that the rates of return on assets can be expressed by possibility distributions rather than probability distributions. We propose two kinds of portfolio selection models based on lower and upper possibilistic means and possibilistic variances, respectively, and introduce the notions of lower and upper possibilistic efficient portfolios. We also present an algorithm which can derive the explicit expression of the possibilistic efficient frontier for the possibilistic mean-variance portfolio selection problem dealing with lower bounds on asset holdings.     

A portfolio optimization model with three objectives and discrete variables

We formulate the portfolio selection as a tri-objective optimization problem so as to find tradeoffs between risk, return and the number of securities in the portfolio. Furthermore, quantity and class constraints are introduced into the model in order to limit the proportion of the portfolio invested in assets with common characteristics and to avoid very small holdings. Since the proposed portfolio selection model involves mixed integer decision variables and multiple objectives finding the exact efficient frontier may be very hard. Nevertheless, finding a good approximation of the efficient surface which provides the investor with a diverse set of portfolios capturing all possible tradeoffs between the objectives within limited computational time is usually acceptable. We experiment with the current state of the art evolutionary multiobjective optimization techniques, namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm (PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), for solving the mixed-integer multiobjective optimization problem and provide a performance comparison among them using metrics proposed by the community.     

最优证券组合的结构特征研究

在库恩－塔克条件基础上，研究了马尔科维茨理论框架内最优证券组合的结构特征，进－步扩展了关于最优证券组合结构特征和有效边界形状的现有成果。     

Decentralised controller structure design and retrofit of process systems based on graph theory

A relative degree matrix-based design method is proposed in this article by using graph theoretical methods for optimal control structure design consisting of single input–single output control loops. This approach enables us to use an efficient algorithm for finding a maximum weighted matching to solve the controller structure selection problem. The resulting optimal structures have been refined by analysing the zero dynamics of the input–output pairs. A novel method for decentralised controller structure retrofit is also proposed in this article. A graph theoretic algorithm is developed, which is based on finding the closest weighted maximum matching. Possible changes in efficiency in the controller structure, which may arise after retrofit, are illustrated using a heat exchanger network retrofit case study.     

Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection

In this paper, we consider a recently proposed model for portfolio selection, called Mean-Downside Risk-Skewness (MDRS) model. This modelling approach takes into account both the multidimensional nature of the portfolio selection problem and the requirements imposed by the investor. Concretely, it optimizes the expected return, the downside-risk and the skewness of a given portfolio, taking into account budget, bound and cardinality constraints. The quantification of the uncertain future return on a given portfolio is approximated by means of LR-fuzzy numbers, while the moments of its return are evaluated using possibility theory. The main purpose of this paper is to solve the MDRS portfolio selection model as a whole constrained three-objective optimization problem, what has not been done before, in order to analyse the efficient portfolios which optimize the three criteria simultaneously. For this aim, we propose new mutation, crossover and reparation operators for evolutionary multi-objective optimization, which have been specially designed for generating feasible solutions of the cardinality constrained MDRS problem. We incorporate the operators suggested into the evolutionary algorithms NSGAII, MOEA/D and GWASF-GA and we analyse their performances for a data set from the Spanish stock market. The potential of our operators is shown in comparison to other commonly used genetic operators and some conclusions are highlighted from the analysis of the trade-offs among the three criteria.     

基于并行遗传算法的气球力Snake模型参数优化

针对气球力Snake模型的图像分割效果很大限度上依赖于初始参数的选取,借鉴遗传算法的高效、并行和全局搜索的性能,提出了一种求解气球力Snake模型最优参数的算法。该算法用气球力Snake能量泛函作为目标函数,引入图像相似度函数作为遗传迭代终止准则,采用并行遗传计算进行分割参数寻优。实际医学图像的实验结果表明,算法能避免通过大量实验来人工选取参数的繁琐,也解决了参数选取不当导致的分割结果不理想的问题,可以得到较好的分割效果。     

The effect of synergy enhancement on information technology portfolio selection

This paper investigates how firms can use synergy to optimize their information technology portfolios. We begin by developing a framework for the portfolio selection by identifying three types of information technology synergy. Next, we use this framework to examine the impact of different types of synergy on the portfolio selection. Analytical models are developed to illustrate the roles of different types of the synergy, and analytical and computational methods are used to investigate the impact of the synergy. The analysis in this paper provides conditions in which synergy enhancement results in a more efficient or a less efficient portfolio. Our study establishes that firms with higher risk thresholds are more likely to obtain more efficient information technology portfolios by enhancing synergy, whereas firms with lower risk thresholds are less likely to benefit from enhancing synergy.     

Extended omega ratio optimization for risk‐averse investors

The omega ratio, a performance measure, is the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. It has been exhibited that the omega ratio optimization is equivalent to a linear program under a mild condition and thus easily tractable. But the omega ratio optimization fails to hedge against many other risks involved in portfolio return that may adversely affect the interests of a risk‐averse investor. On the other hand, there are widely accepted mean‐risk models for portfolio selection that seek to maximize mean return and minimize the associated risk but in general fail to maximize the relative performance ratio around the threshold return. In this paper, we aim to propose a model called ‘extended omega ratio optimization’ that combines the features of the omega ratio optimization model and mean‐risk models. The proposed model introduces constraint on a general risk function in the omega ratio optimization model in such a way that the resultant model remains linear and thus tractable. Our empirical experience with real data from S&P BSE sensex index shows that the optimal portfolios from the extended omega ratio optimization model(s) improved over the optimal portfolios from the omega ratio optimization in having less associated risk and over the optimal portfolios from the corresponding mean‐risk model(s) in having a high value omega ratio.     

Distributing weights under hierarchical clustering: A way in reducing performance breakdown

This paper proposes a clustering asset allocation scheme which provides better risk-adjusted portfolio performance than those obtained from traditional asset allocation approaches such as the equal weight strategy and the Markowitz minimum variance allocation. The clustering criterion used, which involves maximization of the in-sample Sharpe ratio (SR), is different from traditional clustering criteria reported in the literature. Two evolutionary methods, namely Differential Evolution and Genetic Algorithm, are employed to search for such an optimal clustering structure given a cluster number. To explore the clustering impact on the SR, the in-sample and the out-of-sample SR distributions of the portfolios are studied using bootstrapped data as well as simulated paths from the single index market model. It was found that the SR distributions of the portfolios under the clustering asset allocation structure have higher mean values and skewness but approximately the same standard deviation and kurtosis than those in the non-clustered case. Genetic Algorithm is suggested as a more efficient approach than Differential Evolution for the purpose of solving the clustering problem.     

Parallel machine selection and job scheduling to minimize machine cost and job tardiness

This paper discusses the problem of simultaneously selecting and scheduling parallel machines to minimize the sum of machine holding cost and job tardiness cost. A combinatorial optimization model is developed for this purpose. Solving the developed model is NP-hard. A heuristic algorithm is developed to locate the optimal or near optimal solutions based on a Tabu search mechanism specially designed to control the search process in the solution neighborhood for jobs scheduled on specific machines. Numerical examples show that the solutions of the model lead to compromises between the system cost related to machine selection and the operational cost related to job tardiness penalties. The examples also show that the developed algorithm is effective and computationally efficient.     

Heuristic Optimization Methods for Dynamic Panel Data Model Selection: Application on the Russian Innovative Performance

Innovations, be they radical new products or technology improvements, are widely recognized as a key factor of economic growth. To identify the factors triggering innovative activities is a main concern for economic theory and empirical analysis. As the number of hypotheses is large, the process of model selection becomes a crucial part of the empirical implementation. The problem is complicated by unobserved heterogeneity and possible endogeneity of regressors. A new efficient solution to this problem is suggested, applying optimization heuristics, which exploits the inherent discrete nature of the model selection problem. The method is applied to Russian regional data within the framework of a log-linear dynamic panel data model. To illustrate the performance of the method, we also report the results of Monte-Carlo simulations.