An adaptive portfolio trading system: A risk-return portfolio optimization using recurrent reinforcement learning with expected maximum drawdown

Dynamic control theory has long been used in solving optimal asset allocation problems, and a number of trading decision systems based on reinforcement learning methods have been applied in asset allocation and portfolio rebalancing. In this paper, we extend the existing work in recurrent reinforcement learning (RRL) and build an optimal variable weight portfolio allocation under a coherent downside risk measure, the expected maximum drawdown, E(MDD). In particular, we propose a recurrent reinforcement learning method, with a coherent risk adjusted performance objective function, the Calmar ratio, to obtain both buy and sell signals and asset allocation weights. Using a portfolio consisting of the most frequently traded exchange-traded funds, we show that the expected maximum drawdown risk based objective function yields superior return performance compared to previously proposed RRL objective functions (i.e. the Sharpe ratio and the Sterling ratio), and that variable weight RRL long/short portfolios outperform equal weight RRL long/short portfolios under different transaction cost scenarios. We further propose an adaptive E(MDD) risk based RRL portfolio rebalancing decision system with a transaction cost and market condition stop-loss retraining mechanism, and we show that the proposed portfolio trading system responds to transaction cost effects better and outperforms hedge fund benchmarks consistently.     

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.     

Portfolio management system in equity market neutral using reinforcement learning

Portfolio management involves position sizing and resource allocation. Traditional and generic portfolio strategies require forecasting of future stock prices as model inputs, which is not a trivial task since those values are difficult to obtain in the real-world applications. To overcome the above limitations and provide a better solution for portfolio management, we developed a Portfolio Management System (PMS) using reinforcement learning with two neural networks (CNN and RNN). A novel reward function involving Sharpe ratios is also proposed to evaluate the performance of the developed systems. Experimental results indicate that the PMS with the Sharpe ratio reward function exhibits outstanding performance, increasing return by 39.0% and decreasing drawdown by 13.7% on average compared to the reward function of trading return. In addition, the proposed PMS_CNN model is more suitable for the construction of a reinforcement learning portfolio, but has 1.98 times more drawdown risk than the PMS_RNN. Among the conducted datasets, the PMS outperforms the benchmark strategies in TW50 and traditional stocks, but is inferior to a benchmark strategy in the financial dataset. The PMS is profitable, effective, and offers lower investment risk among almost all datasets. The novel reward function involving the Sharpe ratio enhances performance, and well supports resource-allocation for empirical stock trading.

     

A new multi-period investment strategies method based on evolutionary algorithms

This work introduces a new algorithmic trading method based on evolutionary algorithms and portfolio theory. The limitations of traditional portfolio theory are overcome using a multi-period definition of the problem. The model allows the inclusion of dynamic restrictions like transaction costs, portfolio unbalance, and inflation. A Monte Carlo method is proposed to handle these types of restrictions. The investment strategies method is introduced to make trading decisions based on the investor’s preference and the current state of the market. Preference is determined using heuristics instead of theoretical utility functions. The method was tested using real data from the Mexican market. The method was compared against buy-and-holds and single-period portfolios for metrics like the maximum loss, expected return, risk, the Sharpe’s ratio, and others. The results indicate investment strategies perform trading with less risk than other methods. Single-period methods attained the lowest performance in the experiments due to their high transaction costs. The conclusion was investment decisions that are improved when information providing from many different sources is considered. Also, profitable decisions are the result of a careful balance between action (transaction) and inaction (buy-and-hold).

     

A bi-level programming framework for identifying optimal parameters in portfolio selection

This paper addresses the problem of identifying optimal portfolio parameters in nonsparse and sparse models. Generally, using the sample estimates to construct a mean–variance portfolio often leads to undesirable portfolio performance. We propose a novel bi-level programming framework to identify the optimal values of expected return and cardinality, which can be estimated separately or simultaneously. In the general formulation of our approach, outer-level is designed to maximize the utility of the portfolio, which is measured by Sharpe ratio, while the inner-level is to minimize the risk of a portfolio under a given expected return. Considering the nonconvex and nonsmooth characteristics of the outer-level, we develop a hybrid derivative-free optimization algorithm embedded with alternating direction method of multipliers to solve the problem. Numerical experiments are carried out based on both simulated and real-life data. During the process, we give a prior range of cardinality using the data-driven method to promote the efficiency. Estimating the parameters by our approach achieves better performance both in the stock and fund-of-funds markets. Moreover, we also demonstrate that our results are robust when the risk is measured by conditional value-at-risk.     

Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?

Most dynamic programming methods deployed in the portfolio choice literature involve recursions on an approximated value function. The simulation-based method proposed recently by Brandt, Goyal, Santa-Clara, and Stroud (Review of Financial Studies, 18, 831–873, 2005), relies instead on recursive uses of approximated optimal portfolio weights. We examine the relative numerical performance of these two approaches. We show that when portfolio weights are constrained by short sale restrictions for example, iterating on optimized portfolio weights leads to superior results. Value function iterations result in a lower variance but disproportionately higher bias of the solution, especially when risk aversion is high and the investment horizon is long.     

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.     

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.     

A new perspective for optimal portfolio selection with random fuzzy returns

The aim of this paper is to solve the portfolio selection problem when security returns contain both randomness and fuzziness. Utilizing a different perspective, this paper gives a new definition of risk for random fuzzy portfolio selection. A new optimal portfolio selection model is proposed based on this new definition of risk. A new hybrid intelligent algorithm is designed for solving the new optimization problem. In the proposed new algorithm, neural networks are employed to calculate the expected value and the chance value. These greatly reduce the computational work and speed up the process of solution as compared with the random fuzzy simulation used in our previous algorithm. A numerical example is also presented to illustrate the new modelling idea and the proposed new algorithm.     

Using genetic algorithm to support clustering-based portfolio optimization by investor information

A clustering-based portfolio optimization scheme that employs a genetic algorithm (GA) based on investor information for active portfolio management is presented. Whereas numerous studies have investigated trading behaviors, investor performance, and portfolio investment strategies, few works have developed investment strategies based on investor information. This study is conducted in two phases. First, a basket of portfolio (i.e., a collection of stocks held in individual portfolios) is developed through a cluster analysis of investor information. A GA is then employed to optimize the weights of the selected stocks. And the optimized portfolio is rebalanced to get excess return. It is concluded that the proposed multistage portfolio optimization scheme for active portfolio management generates superior results than previously proposed methods for the Korean stock market.     

基于组合算法的RBF神经网络列车轮对缺陷识别

提出了一种基于动态聚类和遗传算法相结合的组合RBF网络训练方法;采用动态聚类法对样本数据进行聚类,使RBF神经网络的隐含层节点中心数在训练过程中自动确定,使用经验公式作为标准,选取最优聚类数,采用遗传算法对隐层中心和宽度以及隐层到输出层的权值进行优化,在全局范围内寻找网络的最优模型;最后对轮对缺陷进行纹理特征提取,并组成训练样本和测试样本,输入到网络进行训练与测试;实验结果表明,与传统方法比较,该组合方法具有较高的识别率。     

Robust optimal decisions with imprecise forecasts

A robust minimax approach for optimal investment decisions with imprecise return forecasts and risk estimations in financial portfolio management is considered. Single-period and multi-period mean-variance optimization models are extended to worst-case design with multiple rival risk estimations and return forecasts. In multi-period stochastic formulation of classical mean-variance portfolio optimization problem, an investor makes an investment decision based on expectations and/or scenarios up to some intermediate times prior to the horizon and, consequently, rebalances or restructures the portfolio. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretized estimate of uncertainties and associated probabilities in future stages. It is well known that return forecasts and risk estimations are inherently inaccurate and there are different rival estimates, or scenario trees. Robust optimization models are presented and imprecise nature of moment forecasts to reduce the risk of making a decision based on the wrong scenario is addressed. The worst-case performance is guaranteed in view of all rival risk and return scenarios and will only improve when any scenario other than the worst-case is realized. The ex-ante performance of minimax models is tested using historical data and backtesting results are presented.     

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。     

Heuristics for the selection of weights in sequential feed-forward neural networks: An experimental study

The selection of weights of the new hidden units for sequential feed-forward neural networks (FNNs) usually involves a non-linear optimization problem that cannot be solved analytically in the general case. A suboptimal solution is searched heuristically. Most models found in the literature choose the weights in the first layer that correspond to each hidden unit so that its associated output vector matches the previous residue as best as possible. The weights in the second layer can be either optimized (in a least-squares sense) or not. Several exceptions to the idea of matching the residue perform an (implicit or explicit) orthogonalization of the output vectors of the hidden units. In this case, the weights in the second layer are always optimized. An experimental study of the aforementioned approaches to select the weights for sequential FNNs is presented. Our results indicate that the orthogonalization of the output vectors of the hidden units outperforms the strategy of matching the residue, both for approximation and generalization purposes.     

Review of urban storm water models

This paper reviews models for simulating storm water quantity and quality in an urban environment. This has been achieved by examining a number of storm water models in current use. The important features of twelve models, which represent a wide range of capabilities and spatial and temporal resolution have been described. Specific topics covered are: identifying important urban water quality parameters; the classification of modelling approaches; modelling approaches used to estimate water quantity and quality. These include statistical, empirical, hydraulic and hydrological models. Water resources management and planning tools, that are included in some urban storm water models, such as economic analysis, optimisation and risk analysis are also discussed. Features of twelve storm water models have been summarised. These models have been chosen because they demonstrate how components that are important in managing urban storm water have been incorporated in a modelling framework. These models have been categorised in terms of their functionality, accessibility, water quantity and quality components included in the model and their temporal and spatial scale. The information in this paper provides planners and managers with an overview of modelling approaches that have been used to simulate storm water quantity and quality. In particular, it provides managers with an appreciation of the limitations and assumptions made in various modelling approaches. This review will also benefit modellers by providing a comprehensive summary of approaches and capabilities of a number of storm water models in current use. Potential urban storm water research opportunities have also been identified.     

Portfolio optimization when risk factors are conditionally varying and heavy tailed

Assumptions about the dynamic and distributional behavior of risk factors are crucial for the construction of optimal portfolios and for risk assessment. Although asset returns are generally characterized by conditionally varying volatilities and fat tails, the normal distribution with constant variance continues to be the standard framework in portfolio management. Here we propose a practical approach to portfolio selection. It takes both the conditionally varying volatility and the fat-tailedness of risk factors explicitly into account, while retaining analytical tractability and ease of implementation. An application to a portfolio of nine German DAX stocks illustrates that the model is strongly favored by the data and that it is practically implementable.     

Communicative action-based business process and information systems modelling with DEMO

Abstract. Abstract. The field of communicative action-based modelling of business processes and information systems has attracted more and more attention in recent years. Inspired by the seminal work of Winograd and Flores, researchers have proposed several modelling approaches. In this article we discuss communicative action-based modelling approaches in general and the DEMO (dynamic essential modelling of organizations) approach in particular. Besides establishing the theoretical foundations of this modelling approach, we also apply DEMO to a case study, and we discuss how the resulting models can be used for information systems design and business process optimization.     

Neuro-evolutionary modelling of the electrodeposition stage of a polymer-supported ultrafiltration–electrodeposition process for the recovery of heavy metals

This paper presents a neuro-evolutionary modelling methodology applied to an electrodeposition process for the recovery of copper and zinc. This technique consists in designing the optimal neural network model using an algorithm obtained through the combination of a multi-objective evolutionary algorithm (NSGA-II) and a local search algorithm (Quasi-Newton). Parametric and structural optimization for feed-forward neural networks are performed determining the optimum number of hidden layers and hidden neurons, the optimum weights and the most appropriate activation functions for the hidden and output layers. Accurate results are obtained in the modelling procedure, with the possibility to choose the adequate model, representing a compromise between performance and complexity. Significant information is obtained by simulation, related to the rate and quality of the electrodeposition process depending of the working conditions. The highest accuracy of the model is obtained for the prediction of copper and zinc concentrations (the most important output variables), a promising result to use the proposed model for the future optimization of the process. Moreover, due to the very different behaviour of copper and zinc in the electrodeposition process, the proposed model could be also successfully used for a wide variety of heavy metal ions.     

状态变化下的连续时间动态投资组合选择

运用两状态隐马尔可夫模型刻画金融资产收益率序列的非线性变化,建立状态变化下的连续时间动态投资组合模型,利用动态规划得到最优投资决策的一般解,使用蒙特卡罗方法模拟投资者的投资决策行为.仿真结果表明:状态变化产生了对冲需求,对冲组合的大小依赖于投资者对市场状态的预期;当风险资产的波动率越小时,投资者状态信念的轻微变化都会引起对冲组合较大幅度的变化;当风险厌恶程度越大时,对冲组合对初始状态信念的变化越不敏感.     

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.