Option contract strategies with risk‐aversion and emergency purchase

This paper considers a one‐period supply chain consisting of a risk‐averse retailer and a risk‐neutral supplier. As a Stackelberg leader, the supplier produces short life‐cycle products to the retailer and determines the option price. The newsvendor‐like retailer orders call option from the supplier with an emergency order opportunity. The analytical model shows that when the emergency purchase price is low, the risk‐averse retailer's optimal order quantity is less than that of a risk‐neutral retailer and independent of the retail price. It is surprising that when it is moderate or high, the risk‐averse retailer may order less than, equal to, or more than a risk‐neutral one. Computational studies are given to investigate the key parameters on optimal decisions and profits. It shows a risk‐averse retailer may get higher profit than a risk‐neutral one. The retailer benefits from a low emergency purchase price, while it harms the supplier.     

A class of linear interval programming problems and its application to portfolio selection

This paper discusses a class of linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem. Considering the uncertain returns of assets in capital markets as intervals, we propose a model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper. The method is illustrated by solving a simplified portfolio selection problem.     

MGP-INTACTSKY: Multitree Genetic Programming-based learning of INTerpretable and ACcurate TSK sYstems for dynamic portfolio trading

In this paper, a Multitree Genetic Programming-based method is developed to learn an INTerpretable and ACcurate Takagi-Sugeno-Kang (TSK) fuzzy rule based sYstem (MGP-INTACTSKY) for dynamic portfolio trading. The MGP-INTACTSKY utilizes a TSK model with a new structure to develop a more interpretable and accurate system for dynamic portfolio trading. In the new structure of TSK, disjunctive normal form rules with variable structured consequent parts are developed in which the absence of some input variables is allowed. Input variables are the most influential technical indices which are selected by stepwise regression analysis. The technical indices are computed using wavelet transformed stock price series to eliminate the noise. The proposed system directly induces the preferred portfolio weights from the stock's technical indices through time. Here, genetic programming with the multitree structure is applied to learn the TSK fuzzy rule bases with the Pittsburgh approach. With this approach, the correlation of different stocks is properly considered during the evolutionary process. To evaluate the performance of the MGP-INTACTSKY for portfolio trading, the proposed model is implemented on the Tehran Stock Exchange as an emerging market as well as Toronto and Frankfurt Stock Exchanges as two mature markets. The experimental results show that the proposed model outperforms other methods such as the momentum strategy, the multitree genetic programming-based crisp system, the genetic algorithm-based first order TSK system, the buy and hold approach and the market's main index in terms of accuracy and interpretability.     

A Multiagent Approach to Q-Learning for Daily Stock Trading

The portfolio management for trading in the stock market poses a challenging stochastic control problem of significant commercial interests to finance industry. To date, many researchers have proposed various methods to build an intelligent portfolio management system that can recommend financial decisions for daily stock trading. Many promising results have been reported from the supervised learning community on the possibility of building a profitable trading system. More recently, several studies have shown that even the problem of integrating stock price prediction results with trading strategies can be successfully addressed by applying reinforcement learning algorithms. Motivated by this, we present a new stock trading framework that attempts to further enhance the performance of reinforcement learning-based systems. The proposed approach incorporates multiple Q-learning agents, allowing them to effectively divide and conquer the stock trading problem by defining necessary roles for cooperatively carrying out stock pricing and selection decisions. Furthermore, in an attempt to address the complexity issue when considering a large amount of data to obtain long-term dependence among the stock prices, we present a representation scheme that can succinctly summarize the history of price changes. Experimental results on a Korean stock market show that the proposed trading framework outperforms those trained by other alternative approaches both in terms of profit and risk management.     

大数据分析的应用案例——投资模型的稳健性

交易模型的稳健性,指的是该模型的利润率曲线的波动性较小,没有大起大落。针对一个基于支持向量回归（SVR）技术的算法交易模型的稳健性问题,提出了使用若干导出指标训练统一的交易模型的策略,以及投资组合多样化的方法。首先,介绍基于支持向量回归技术的算法交易模型;然后,基于常用指标,构造了若干导出指标,用于股票价格的短期预测。这些指标,刻画了近期价格运动的典型模式、超买/超卖市场状态,以及背离市场状态。对这些指标进行了规范化,用于训练交易模型,使得模型可以泛化到不同的股票;最后,设计了投资组合多样化方法。在投资组合里,各个股票之间的相关性,有时会导致较大的投资损失;因为具有较强相关关系的股票,其价格朝相同方向变化。如果交易模型预测的价格走势不正确,引起止损操作,那么这些具有较强相关关系的股票,将引发雪崩式的止损,于是导致损失加剧。把股票根据相似性聚类到不同类别,通过从不同聚类类别中选择若干股票来构成多样化的投资组合,其中,股票的相似性,通过交易模型在不同股票上近期的利润曲线的相似度进行计算。在900只股票10年的价格大数据上进行了实验,实验结果显示,交易模型能够获得超过定期存款的超额利润率,年化利润率为8.06%。交易模型的最大回撤由13.23%降为5.32%,夏普指数由81.23%提高到88.79%,交易模型的利润率曲线波动性降低,说明交易模型的稳健性获得了提高。     

结束时间不确定的投资组合选择问题建模与模型求解方法

针对结束时间具有不确定性的投资问题,建立以区间风险值(PVaR)度量市场风险的收益最大化投资组合选择模型.PVaR计算的复杂性使得模型难以运用一般优化方法求解,因此提出并证明可以通过求解等效的混合整数规划模型来得到原模型的最优解.利用实际股价数据进行数值实验分析,结果表明,求解混合整数规划模型针对小规模短期投资问题可以快速给出最优投资决策方案.     

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。     

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.     

Optimal algorithms for trading large positions

In this paper, we are concerned with the problem of efficiently trading a large position on the market place. If the execution of a large order is not dealt with appropriately this will certainly break the price equilibrium and result in large losses. Thus, we consider a trading strategy that breaks the order into small pieces and execute them over a predetermined period of time so as to minimize the overall execution shortfall while matching or exceeding major execution benchmarks such as the volume-weighted average price (VWAP). The underlying problem is formulated as a discrete-time stochastic optimal control problem with resource constraints. The value function and optimal trading strategies are derived in closed form. Numerical simulations with market data are reported to illustrate the pertinence of these results.     

Reduction of the two-step problem of stochastic optimal control with bilinear model to the problem of mixed integer linear programming

Consideration was given to the two-step problem of stochastic optimization with a bilinear model which describes the problem of forming the securities portfolio consisting of some risk assets and one riskless asset. The probability of exceeding the given threshold of capital is used as the optimality criterion. At the second step, the piecewise constant control is used as the capital control. Determined were the upper and lower estimates of the probability functional. The problems of maximizing the upper and lower estimates of the probability functional were reduced to the problems of mixed integer linear programming by means of discretizing the probabilistic measure. An algorithm to seek an approximate solution to the original problem was proposed, and an example was considered.     

A modular Decision Support System for optimum investment selection in presence of uncertainty: Combination of fuzzy mathematical programming and fuzzy rule based system

In this paper, we have developed a modular Decision Support System (DSS) in order to select an optimum portfolio of several chances for investments in presence of uncertainty. The investments are considered as the projects so as their initial investment costs, profits, resource requirement, and total available budget are assumed to be uncertain. This uncertainty has been modeled using fuzzy concepts. The proposed DSS has two main modules. The first one is a fuzzy binary programming model which represents the mathematical model of the associated fuzzy capital-budgeting problem. It involves finding optimum combination of investment portfolio considering a multi-objective measurement function and subject to several set of constraints. The results of optimistic and pessimistic analysis of the aforementioned fuzzy binary programming model plus a managerial Confidence Level (CL) value are treated as input of a fuzzy rule based system which is the second module of the proposed DSS. Although some projects are simple to make a decision about at the final step of the first module but the unique output of the second module of the proposed DSS is Risk of Investment (ROI) for all remained project. The logic relations between precedence parts of the rules as well as CL value will work in favor of computational efforts in second module through diminishing some unessential rules. This will help to define a complete set of fuzzy IF-THEN rules more efficiently. The proposed DSS can help the decision makers to select an optimum investment portfolio with minimum risk in a complete ambiguous condition.     

基于预期完成率的月内滚动机组组合研究

为保障月度交易计划执行,提出了一种基于预期完成率的月内滚动机组组合方法,实现机组开停方式、电量计划完成情况和后续供需形势之间的有效匹配。为避免发电机组开停方式频繁调整,定义了发电厂预期完成率评价指标,以量化原发电机组组合方式下电量计划执行风险。若执行风险超过预期,则启动月内滚动机组组合。月内滚动机组组合以保障月度交易计划执行且各发电厂完成率均衡为优化目标,综合考虑电力电量平衡、网络传输能力、机组出力范围等约束约束,能够对当月后续运行日的发电机组组合方式优化调整。最后,基于IEEE-30节点系统构造的算例表明,预期完成率指标能够避免发电机组组合方式的频繁调整,保障发电厂月度交易计划可靠执行。     

Mean-variance-skewness model for portfolio selection with transaction costs

A mean-variance-skewness model is proposed for portfolio selection with transaction costs. It is assumed that the transaction cost is a V-shaped function of the difference between the existing portfolio and a new one. The mean-variance-skewness model is a non-smooth programming problem. To overcome the difficulty arising from non-smoothness, the problem was transformed into a linear programming problem. Therefore, this technique can be used to solve large-scale portfolio selection problems. A numerical example is used to illustrate that the method can be efficiently used in practice.     

具有联合椭圆不确定集与概率约束的鲁棒投资组合选择

针对参数在一个联合椭圆不确定集中变化的情形,建立了一个具有概率约束的鲁棒投资组合模型,并将其转化为可由内点算法求解的含线性矩阵不等式(LMI)约束的凸规划问题.应用实际交易数据对所提出的模型进行数值实验和比较,结果表明此模型能够获得具有更好财富增长率的投资策略,并能有效地分散最优投资组合的风险.     

Stock Trading Using RSPOP: A Novel Rough Set-Based Neuro-Fuzzy Approach

This paper investigates the method of forecasting stock price difference on artificially generated price series data using neuro-fuzzy systems and neural networks. As trading profits is more important to an investor than statistical performance, this paper proposes a novel rough set-based neuro-fuzzy stock trading decision model called stock trading using rough set-based pseudo outer-product (RSPOP) which synergizes the price difference forecast method with a forecast bottleneck free trading decision model. The proposed stock trading with forecast model uses the pseudo outer-product based fuzzy neural network using the compositional rule of inference [POPFNN-CRI(S)] with fuzzy rules identified using the RSPOP algorithm as the underlying predictor model and simple moving average trading rules in the stock trading decision model. Experimental results using the proposed stock trading with RSPOP forecast model on real world stock market data are presented. Trading profits in terms of portfolio end values obtained are benchmarked against stock trading with dynamic evolving neural-fuzzy inference system (DENFIS) forecast model, the stock trading without forecast model and the stock trading with ideal forecast model. Experimental results showed that the proposed model identified rules with greater interpretability and yielded significantly higher profits than the stock trading with DENFIS forecast model and the stock trading without forecast model.     

A programming approach for nonsmooth structural optimization

A two-level programming algorithm for some nonsmooth structural optimization problems is presented. When an optimization problem has both stress and unilateral displacement constraints, we combine the structural optimization with unilateral analysis to formulate a two-level model. Quadratic programming (QP) is used in analysis level, which is solved with dual interior-point method, and linear programming (LP) is used in optimization level. Several examples with unilateral or bilateral constraints are provided to verify the proposed algorithm.     

On multiobjective combinatorial optimization and dynamic interim hedging of efficient portfolios

A dynamic portfolio policy is one that periodically rebalances an optimally diversified portfolio to account for time‐varying correlations. In order to sustain target‐level Sharpe performance ratios between rebalancing points, the efficient portfolio must be hedged with an optimal number of contingent claim contracts. This research presents a mixed‐integer nonlinear goal program (MINLGP) that is directed to solve the hierarchical multiple goal portfolio optimization model when the decision maker is faced with a binary hedging decision between portfolio rebalance periods. The MINLGP applied to this problem is formed by extending the separable programming foundation of a lexicographic nonlinear goal program (NLGP) to include branch‐and‐bound constraints. We establish the economic efficiency of applying this normative approach to dynamic portfolio rebalancing by comparing the risk‐adjusted performance measures of a hedged optimal portfolio to those of a naively diversified portfolio. We find that a hedged equally weighted small portfolio and a hedged efficiently diversified small portfolio perform similarly when comparing risk‐adjusted return metrics. However, when percentile risk measures are used to measure performance, the hedged optimally diversified portfolio clearly produces less expected catastrophic loss than does its nonhedged and naively diversified counterpart.     

A new approach for selecting portfolio of new product development projects

The most decisive factor that survives enterprises under stiff competition is the development of new product (NPD), and when entering the product development stage after the fuzzy front end, a best project portfolio should be finalized in order to potentially create expected revenue and competitive advantage. However, even it reaches the end of the fuzzy front stage; the NPD project is still significantly involved with uncertainties, complexities and fuzziness. To assist R&D managers making decision in this environment, this study proposes a new approach which combines fuzzy set theory and multi-criteria group decision making method into a NPD project portfolio selection model. This model takes into account project performance, project delivery and project risk, and formulates the selection decision of NPD project portfolio as a fuzzy linear programming problem. The illustrative example shows that the model proposed can generate projects with the highest success rate under limited resources and manpower.     

基于以太坊和动态定价的数据交易模式研究

为了解决现有数据交易模式中交易流程耗时较大且效率较低,信息泄露和公平支付问题,提出一种改进的数据交易模式,通过智能合约预置额外的约束条件,集成了数据交易和仲裁纠纷解决的功能,用于实现交易的公平自治性和交易时间控制,以规避数据交易过程中恶意交易行为。在此基础上,为实现所提出的数据交易模式中价格的动态平衡,基于经济建模方法和动态定价的公平合理性,设计一个自动平衡总供给和总需求的动态定价机制,依据购买需求和数据资源的市场供给进行价格动态调整。从模型的动态性对模型进行了论证,证明了交易价格和需求可以收敛。基于以太坊实验环境部署并执行该合约,并对该智能合约的各功能成本和安全性进行测试和分析。仿真实验结果表明,该改进交易模式在动态定价下能够以较低的执行成本进行数据交易,并且该智能合约存在较少代码漏洞,满足可行性和安全性要求。     

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.