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.     

基于粒子群位移转移的混合遗传算法及其应用

基于粒子群位移转移的思想,改变遗传算法的变异规则,提出了一种新的混合遗传算法。利用3个benchmark函数测试了新的混合算法的性能,并将测试结果与标准遗传算法进行了比较。提出了一种多阶段半方差投资选择模型,并将混合算法应用在多阶段半方差投资选择问题的求解上。     

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.     

Models and Simulations for Portfolio Rebalancing

In 1950 Markowitz first formalized the portfolio optimization problem in terms of mean return and variance. Since then, the mean-variance model has played a crucial role in single-period portfolio optimization theory and practice. In this paper we study the optimal portfolio selection problem in a multi-period framework, by considering fixed and proportional transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model, based on the Conditional Value at Risk (CVaR) as measure of risk, to introduce portfolio rebalancing. The aim is to provide investors and financial institutions with an effective tool to better exploit new information made available by the market. We then suggest a procedure to use the proposed optimization model in a multi-period framework. Extensive computational results based on different historical data sets from German Stock Exchange Market (XETRA) are presented.     

多期证券投资组合问题的区间多目标规划求解方法

投资组合问题主要研究如何将有限的资金合理地分配到不同的金融资产中,以实现收益最大化与风险最小化之间的均衡.然而,证券市场往往具有很强的不确定性,投资者对于证券的期望收益率和风险损失率难以用精确数值描述,区间规划则是处理这类不确定性问题的有力工具.鉴于此,首先基于区间多目标规划建立一个以预期收益率、风险损失率和流动性为目标函数的多期投资组合选择模型;然后通过设计一个定向变异算子,改进基于偏好多面体的交互式遗传算法,并将上述算法的运算机制与所建模型的多期特性相结合以求解模型;最后在不确定交互进化优化系统上进行实证分析.实验结果表明,所提出算法能够根据投资者的不同需要得到相应最满意的多期资产组合.     

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.     

Portfolio optimization problems in different risk measures using genetic algorithm

This paper introduces a heuristic approach to portfolio optimization problems in different risk measures by employing genetic algorithm (GA) and compares its performance to mean–variance model in cardinality constrained efficient frontier. To achieve this objective, we collected three different risk measures based upon mean–variance by Markowitz; semi-variance, mean absolute deviation and variance with skewness. We show that these portfolio optimization problems can now be solved by genetic algorithm if mean–variance, semi-variance, mean absolute deviation and variance with skewness are used as the measures of risk. The robustness of our heuristic method is verified by three data sets collected from main financial markets. The empirical results also show that the investors should include only one third of total assets into the portfolio which outperforms than those contained more assets.     

考虑投资者心理特征的模糊投资组合优化模型

投资者在实际金融市场中的决策行为往往会受到主观心理认知的影响.考虑参照依赖、敏感性递减和损失厌恶等影响投资决策的心理特征,研究模糊环境下的投资组合选择问题.首先,假设资产的收益为梯形模糊数,依据前景理论中的价值函数,将组合收益转化为体现投资者心理特征的感知价值;然后,以感知价值的可能性均值最大化和可能性下半方差最小化为目标,建立考虑心理特征的模糊投资组合优化模型;接着,为了有效地求解模型,设计一个多种群遗传算法;最后,通过实例分析表明模型和算法的有效性.结果表明,与传统的遗传算法相比,所设计的多种群遗传算法可更有效地求解模型,考虑心理特征的模糊投资组合优化模型能够提升投资者的满意程度,可为实际的投资活动提供决策支持.     

Selection of a dynamic supply portfolio in make-to-order environment withrisks

The problem of a multi-period supplier selection and order allocation in make-to-order environment in the presence of supply chain disruption and delay risks is considered. Given a set of customer orders for finished products, the decision maker needs to decide from which supplier and when to purchase product-specific parts required for each customer order to meet customer requested due date at a low cost and to mitigate the impact of supply chain risks. The selection of suppliers and the allocation of orders over time is based on price and quality of purchased parts and reliability of supplies. For selection of dynamic supply portfolio a mixed integer programming approach is proposed to incorporate risk that uses conditional value-at-risk via scenario analysis. In the scenario analysis, the low-probability and high-impact supply disruptions are combined with the high probability and low impact supply delays. The proposed approach is capable of optimizing the dynamic supply portfolio by calculating value-at-risk of cost per part and minimizing expected worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.     

A multi-objective robust possibilistic model for technology portfolio optimization considering social impact and different types of financing

With respect to limited financial resources, prioritization of technology fields in order to be supported financially is a matter of paramount significance that governmental organizations, such as “Technology Development Funds (TDFs)”, face with. Innovation and technology development, as the cornerstone of the economic development of countries, requires making decisions in terms of assigning the best-suited form of financial resources mainly by governments. Accordingly, this study addresses a multi-objective portfolio optimization problem in a multi-period setting with the aim of maximizing the created jobs – as a key factor in social welfare – as well as intended profit while minimizing the risk of inappropriate portfolio selection. To formulate the proposed mathematical model, different financing methods, technology readiness levels (TRL), and return on investment (ROI) associated with each technological project are taken into account. Afterward, to deal with the uncertainty arisen from fuzzy parameters, the Multi-Objective Robust Possibilistic Programming approach (MORPP) is applied, the performance of which is examined under several computational tests. Finally, to illustrate the performance of the proposed model and its applicability in practice, the computational results are shown through a real case study in Iran Innovation & Prosperity Fund (IIPF). The results show that selecting small and medium-sized enterprises (SMEs) for being financed, is the best option when increasing job creation is considered in portfolio optimization. Furthermore, the comparison of the MORPP model results with the deterministic model shows that the solutions obtained from the robust possibilistic approach outweighed the deterministic model.     

Optimal mean–variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean–variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor.     

Generating effective defined-contribution pension plan using simulation optimization approach

This paper presents an optimization approach to analyze the problems of portfolio selection for long-term investments, taking into consideration the specific target replacement ratio for defined-contribution (DC) pension scheme; the purpose is to generate an effective multi-period asset allocation that reaches an amount matching the target liability at retirement date and reduce the downside risk of the investment. A multi-period asset liability simulation model was used to generate 4000 asset return predictions, and an evolutionary algorithm, evolution strategies, was incorporated into the model to generate multi-period asset allocations under four conditions, considering different weights for measuring the importance of matching the target liability and different periods of downside risk measurement. Computational results showed that the evolutionary algorithm, evolution strategies, is a very robust and effective approach to generate promising asset allocations under all the four cases. In addition, computational results showed that the promising asset allocations revealed valuable information, which is able to help fund managers or investors achieve a higher average investment return or a lower level of volatility under different conditions.     

风险资产收益序列相关的多阶段均值-方差投资组合选择

基于多阶段均值-方差框架, 研究任意多种风险资产存在一般收益序列相关时的投资组合选择问题. 首先, 采用Lagrange 对偶原理与动态规划相结合的方法对模型进行求解, 得到多阶段均值-方差模型的有效投资策略和有效边界的解析表达式; 然后, 证明在含有无风险资产的情形下有效边界仍为均值-标准差平面上的一条射线; 最后, 应用所得结论给出一个具体的实例分析.

     

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.     

Possibilistic Approaches to Portfolio Selection Problem with General Transaction Costs and a CLPSO Algorithm

The structure of portfolio selection depends essentially on the form of transaction cost. In this paper, we deal with the portfolio selection problems with general transaction costs under the assumption that the returns of assets obey LR-type possibility distributions. For any type of transaction costs, we employ a comprehensive learning particle swarm optimizer algorithm to obtain the optimal portfolio. Furthermore, we offer numerical experiments of different forms of transaction costs to illustrate the effectiveness of the proposed model and approach.     

Lieferantenportfolio-Management für IT-Services unter Berücksichtigung von Diversifikationseffekten

By means of service-oriented architectures the IT support of processes can be designed as a portfolio of individual IT services provided by different suppliers. The processes are designed based on selection decisions between IT services that potentially have to be included. Many companies formulate a multitude of requirements for investments in IT services at ever shorter intervals. However, the scope of the desired investments usually exceeds the available budget. Thus, companies face the challenge of allocating the limited budget to investments in the most promising combination of IT services. This is hardly possible without methodical support. In addition, the allocation is often done intuitively and subject to the decision-makers?? affinity with IT. Therefore, this paper develops a quantitative, multi-period procedure model for the purpose of maximizing the enterprise value in accordance with value based management, which considers the dependencies of the periodical selection decisions. In the following, a decision logic for the heuristic solution to the selection problem is presented and its application is demonstrated by means of an illustrative case example.     

风险效用投资组合模型的遗传算法求解

给出一个折衷考虑风险最小化和收益最大化的单目标决策方法,以单位风险收益最大化为决策目标建立了投资组合的非线性分式规划模型,考虑到分式规划问题的求解难度,利用遗传算法求解模型,并给出算法步骤。最后,给出了数值算例,结果表明该算法是简单有效的。     

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。     

Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation

For an investor to claim his wealth resulted from his multiperiod portfolio policy, he has to sustain a possibility of bankruptcy before reaching the end of an investment horizon. Risk control over bankruptcy is thus an indispensable ingredient of optimal dynamic portfolio selection. We propose in this note a generalized mean-variance model via which an optimal investment policy can be generated to help investors not only achieve an optimal return in the sense of a mean-variance tradeoff, but also have a good risk control over bankruptcy. One key difficulty in solving the proposed generalized mean-variance model is the nonseparability in the associated stochastic control problem in the sense of dynamic programming. A solution scheme using embedding is developed in this note to overcome this difficulty and to obtain an analytical optimal portfolio policy.