Multi-period Portfolio Selection Problem Research Articles

Learning fused lasso parameters in portfolio selection via neural networks

AbstractIn recent years, fused lasso models are becoming popular in several fields, such as computer vision, classification and finance. In portfolio selection, they can be used to penalize active positions and portfolio turnover. Despite efficient algorithms and software for solving non-smooth optimization problems have been developed, the amount of regularization to apply is a critical issue, especially if we have to achieve a financial aim. We propose a data-driven approach for learning the regularization parameters in a fused lasso formulation of the multi-period portfolio selection problem, able to realize a given financial target. We design a neural network architecture based on recurrent networks for learning the functional dependence between the regularization parameters and the input data. In particular, the Long Short-Term Memory networks are considered for their ability to process sequential data, such as the time series of the asset returns. Numerical experiments performed on market data show the effectiveness of our approach.

An uncertainty theory based tri-objective behavioral portfolio selection model with loss aversion and reference level using a modified evolutionary root system growth algorithm

The outbreak of uncertain events, e.g., financial crisis, regional conflict and abrupt contagion, has a significant impact on residents’ income. Hence, the wealth management and portfolio selection become more and more important. In addition, the behavioral finance believes that decision-making process of the investors not only depend on utility maximization, but also on who to compare with. It differs from the traditional finance based on rational cognitive acquiring and decision-making of agents, in this paper, we consider both investment uncertainty and investment utility with reference level for portfolio selection. First, we introduce the uncertainty theory and loss aversion utility with reference level based on behavioral finance. Then we study an uncertain multi-period portfolio selection problem. Moreover, we formulate an uncertain behavioral portfolio selection model with three objective functions for which we propose an equivalent program consisting of a main model and two auxiliary models for tri-objective optimization model. Thereafter, we use a modified evolutionary root system growth algorithm to solve the transformed models. Finally, a numerical simulation allows to show the practicability of proposed models and validity of modified algorithm.

Regularization methods for sparse ESG-valued multi-period portfolio optimization with return prediction using machine learning

In the context of global sustainable development, environmental, social, and governance (ESG) investment has become a frontier topic in the field of asset management. This paper focuses on ESG-valued multi-period portfolio selection problem which incorporates ESG factor into traditional portfolio optimization. Using ESG-valued returns instead of traditional returns, we propose an ESG-valued fused LASSO model to promote an optimal sparse multi-period portfolio strategy. The objective of the model is to minimize a combination of returns and risks with respect to ESG ratings based on classical Markowitz mean–variance framework. The sparsity of the portfolio at each period and the turnover across periods is achieved by the ℓ1 regularization approach. To improve the out-of-sample performance of the ESG-valued model, we introduce two machine learning methods, namely random forest and support vector regression, to predict the ESG-valued returns. We develop a symmetric alternating direction method of multipliers to solve the regularized optimization model. Additionally, some other sparsity-driven penalty functions are discussed which results in a general framework of multi-period portfolio optimization. Finally, numerical experiments on several real datasets from both in-sample and out-of-sample demonstrate the positive effect of ESG in multi-period portfolio optimization.

An Approach for a Multi-Period Portfolio Selection Problem by considering Transaction Costs and Prediction on the Stock Market

This paper addresses a method to solve a multi-period portfolio selection on the stock market. The portfolio problem seeks an investor to trade stocks with a finite budget and a given integer number of stocks to hold in a portfolio. The trade must be performed through a stockbroker that charges its respective transaction cost and has its minimum required trade amount. A mathematical model has been proposed to deal with the constrained problem. The objective function is to find the best risk-return rate; thus, Sharpe Ratio and Treynor Ratio are used as objective functions. The returns are the same for these ratios, but the risks are not Sharpe considering covariance and Treynor systematical risk. The returns are predicted using a Neural Net with Long-Short-Term Memory (LSTM). This neural net is compared with simple forecasting methods through Mean Absolute Percentage Error (MAPE). Computational experiments show the quality prediction performed by LSTM. The heteroskedastic risk is estimated by Generalized Autoregressive Conditional Heteroskedasticity (GARCH), adjusting the variance for every period; this risk measure is used in Sharpe Ratio. The experiment contemplates a weekly portfolio selection with 5 and 10 stocks in 122 weekly periods for each Chilean market ratio. The best portfolio is Sharpe Ratio with ten stocks, performing a 62.28% real return beating the market, represented by the Selective Stock Price Index (IPSA). Even the worst portfolio, Treynor Ratio, overcomes the IPSA cumulative yield with ten stocks.

Distributionally robust optimization with Wasserstein metric for multi-period portfolio selection under uncertainty

The mean-variance model formulated by Markowitz for a single period serves as a fundamental method of modern portfolio selection. In this study, we consider a multi-period case with uncertainty that better matches the reality of the financial market. Using the Wasserstein metric to characterize the uncertainty of returns in each period, a new distributionally robust mean-variance model is proposed to solve multi-period portfolio selection problem. We further transform the developed model into a tractable convex problem using duality theory. We also apply a nonparametric bootstrap method and provide a specific algorithm to estimate the radius of the Wasserstein ball. The effects of the parameters on the corresponding strategy and evaluation criteria of portfolios are analyzed using in-sample data. The analysis indicate that the return and risk of our portfolio selections are relatively immune to parameter values. Finally, a series of out-of-sample experiments demonstrate that the proposed model is superior to some other models in terms of final wealth, standard deviation, and Sharpe ratio.

An event-triggered iteratively reweighted convex optimization approach to multi-period portfolio selection

This paper addresses multi-period portfolio selection driven by events. We define an event-triggering function to mimic fund managers to activate sequential portfolio rebalancing and maximize Sharpe and Sortino ratios in the Markowitz’s return–risk framework. At first, the multi-period portfolio selection problem is formulated with a variable weight as a series of biconvex optimization problems with a surrogated objective function to maximize the Sharpe ratio or Sortino ratio. In each period, the portfolio optimization problem is further reformulated as an iteratively reweighted convex quadratic optimization problem. The multi-period portfolio selection problem is then solved sequentially based on a defined event-trigger function and a quadratic optimizer. The experiments are done on eight world stock markets datasets to show the capabilities of the proposed approach in calculating market indices and equal-weighted portfolios in terms of Sharpe and Sortino ratios.

Multiagent-based deep reinforcement learning for risk-shifting portfolio management

The growing popularity of quantitative trading in pursuit of a systematic and algorithmic approach to investment has drawn considerable attention among traders and investment firms. Consequently, an effective computational method for evaluating potential risk factors and returns is crucial for the development of algorithmic trading strategies. In traditional finance and financial engineering research, statistical approaches have been widely applied to quantitative analysis. Meanwhile, investor demand for quantitative hedge funds has surged worldwide. In the current study, the multiperiod portfolio selection problem was considered in terms of the realistic transaction cost model, which is a major concern for quantitative hedge fund managers. We developed a dedicated multiagent-based deep reinforcement learning framework with a two-level nested agent structure to determine effective portfolio management methods with different objectives. In addition, we proposed a specially-designed reward function for investment performance evaluation and a novel policy network structure for trading decision-making. To efficiently identify specific asset attributes in a portfolio, each agent is equipped with a refined deep policy network and a special training method that enables the proposed reinforcement learning agent to learn risk transfer behaviors. The results revealed the effectiveness of our proposed framework, which outperformed several established or representative portfolio selection strategies.

An analytic solution for multi-period uncertain portfolio selection problem

An analytic solution for multi-period uncertain portfolio selection problem

Dynamic multi-period sparse portfolio selection model with asymmetric investors’ sentiments

Asymmetric investors’ sentiments on returns and risks play an important role in updating the portfolio strategies in multi-period portfolio selection problems. By introducing the Prospect Theory to measure the asymmetric investors’ sentiments, a dynamic sentiment-adjusted model (DSAM) is proposed to sparse portfolio selection problem over multiple periods, in which the objective is to minimize the risk of the portfolio. As we focus on the sparse portfolio, a l0 constraint is added to our model. The l0 constraint represents that we can only purchase at most k securities from N candidate securities, in which k is a small number compared to N. Since the objective function of the sparse portfolio with l0 constraint is NP-hard, and could not be solved by the Deep Learning algorithms. The stochastic neural networks algorithm with re-parametrisation trick (SNNrP) is introduced to solve the DSAM. The back-testing framework of our paper includes a multi-period portfolio selection model, in which asymmetric investors’ sentiments are modeled to iterate investors’ expected return level each period. In the back-testing framework, we conduct the experiments for different investment periods with different investors’ sentiments. The experimental results for the Nasdaq and CSI 300 data sets show that, on average, compared with the traditional Mean–variance model, the terminal return and risk obtained by the DSAM model outperforms by 9% and 11.75%.

An Examination of Target Date Fund Glidepath Construction

The paper examines Target Date Fund glidepath construction as well as asset allocation strategies. We consider characteristics, features, and assumptions in solving the multi-period portfolio selection problem. This paper discusses the theoretical underpinnings of deterministic, adaptive, and stochastic models as well as some interesting alternative strategies. Furthermore, we also propose research topics for future consideration that the author believes may improve upon the existent model frameworks.

A multiobjective multiperiod mean-semientropy-skewness model for uncertain portfolio selection

Due to the complexity of the financial market, security returns are sometimes expressed by expert estimates rather than historical data. In this paper, we deal with a multiobjective multiperiod portfolio selection problem based on uncertainty theory. We propose a new uncertain multiobjective multiperiod mean-semisentropy-skewness portfolio optimization model, in which uncertain semi-entropy is used to quantify the downside risk. To be more realistic, several constraints are also considered, such as the transaction costs, cardinality, liquidity, budget, and bound constraint. Moreover, a novel hybrid technique, called the MFA-SOS algorithm, which combines the features of the firefly algorithm (FA) and symbiotic organism search algorithm (SOS) is designed to solve the proposed model. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

Mean‐field formulation for the infinite‐horizon mean–variance control of discrete‐time linear systems with multiplicative noises

This study considers the infinite-horizon stochastic optimal control of a discounted and long-run average costs under a mean–variance trade-off performance criterion for discrete-time linear systems subject to multiplicative noises. The authors adopt a mean-field approach to tackle the problem and get an optimal control solution in terms of a set of two generalised coupled algebraic Riccati equations (GCAREs). Then, they establish sufficient conditions for the existence of the maximal solution and necessary and sufficient conditions for the existence of the mean-square stabilising solution to the GCARE. From this solution, they derive optimal control policies to the related discounted and long-run average cost problems. A numerical example illustrates the obtained results for the multi-period portfolio selection problem in which it is desired to minimise the sum of the mean–variance trade-off costs of a portfolio against a benchmark along the time.

A multi-period fuzzy mean-minimax risk portfolio model with investor’s risk attitude

This paper deals with a multi-period portfolio selection problem considering investor’s risk attitude in fuzzy environment. We regard the return rate of each risky asset as a fuzzy number and use the expected value and semi-absolute deviation to measure its return and risk, respectively. We adopt an $$l_{\infty }$$ downside risk function to measure the portfolio’s risk, which is represented by the maximum individual risk. Moreover, we formulate a reasonable diversification constraint for the portfolio involving risk-free asset. Then, we propose a multi-period portfolio selection model with the objectives of maximizing the final expected wealth and minimizing the final cumulative risk. Furthermore, we design a multiple particle swarm optimization to solve it. Finally, we illustrate the effectiveness of the model and algorithm by using a real case.

A mean-field formulation for the mean-variance control of discrete-time linear systems with multiplicative noises

ABSTRACT This paper considers the stochastic optimal control of a multi-period mean-variance trade-off performance criterion with and without constraints for discrete-time linear systems subject to multiplicative noises. We adopt a mean-field approach to tackle the problem and obtain a solution for the unconstrained case in terms of a Riccati-like difference equation. From this general result, we obtain a sufficient condition for a closed-form solution for one of the constrained problems considered in the paper. When particularised to the portfolio selection problem, we show that our results retrieve some of the results available in the literature. We conclude the paper by illustrating the obtained optimal controls with a multi-period portfolio selection problem where we minimise the sum of the mean-variance trade-off costs of a portfolio against a benchmark along the time.

Fuzzy multi-period portfolio selection model with time-varying loss aversion

This paper deals with multi-period portfolio selection problem in a fuzzy environment, in which the effects of investors’ time-varying asymmetric attitudes to losses and gains on portfolio selection are taken into consideration. In the paper, a definition of time-varying loss aversion is presented to describe the aforementioned time-varying asymmetric attitudes to losses and gains. A fuzzy multi-period portfolio selection model based on this new definition of time-varying loss aversion is formulated. Then, an improved co-evolutionary particle swarm optimization (ICPSO) algorithm is designed to solve the proposed model. The comparison analysis between the proposed model and the fixed-parameter loss aversion model is provided to demonstrate the fact that the proposed model can significantly affect the performance of portfolio selection. Finally, a numerical example is given to illustrate the application of the proposed model and the efficiency of the designed algorithm.

Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory

This paper discusses an uncertain multi-period portfolio selection problem in the situation where the future security return rates are given by experts’ estimations instead of historical data. In financial market, investors may have different attitudes towards risk for different goals. In order to reflect these conflicting risk attitudes for different goals, mental accounts are introduced to the investment. In addition, investment strategies may be affected by some realistic constraints such as background risk, liquidity risk, transaction cost and cardinality constraint. Based on uncertainty theory, a nonlinear multi-period portfolio selection model is proposed with consideration of mental accounts and realistic constraints. In the model, indeterminate quantities such as security return rates and turnover rates are assumed to be uncertain variables. Within the framework of uncertainty theory, we discuss the equivalents of the model and show that the nonlinear model can be equivalently transformed into a linear programming model. Finally, a case study is given to illustrate the performance of the proposed model.

Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models

There are myriad works that deal with the fuzzy multi-period portfolio selection problem, but when we talk about multi-period portfolio selection in an intuitionistic fuzzy realm, to the best of our knowledge, there is no research work that deals with the same. So, to fill this research gap, we propose an intuitionistic fuzzy multi-period portfolio selection model with the objectives of maximization of the terminal wealth and minimization of the cumulative risk subject to several realistic constraints such as complete capital utilization, no short selling, fixed transaction costs for buying and selling, bounds on the desired returns of each period, cardinality constraint, and bounds on the minimal and the maximal proportion of the capital allocated to an asset. The membership and non-membership of the objectives are modeled using their extreme values. The proposed approach provides avenues for the inclusion and minimization of the hesitation degree into decision making, thereby resulting in a significantly better portfolio. Parameters $$\theta _W$$ and $$\theta _{Va}$$ are used to introduce the hesitation in the model, and, based on their values, the model is further categorized into optimistic and pessimistic intuitionistic fuzzy multi-period portfolio selection models for optimistic and pessimistic investors, respectively. The max–min approach is used to solve the proposed models. Furthermore, a numerical illustration is presented to exhibit the virtues of the proposed model.

Multi-period mean-variance portfolio selection with practical constraints using heuristic genetic algorithms

Since Markowitz proposed the mean-variance (MV) formulation in 1952, it has been used to configure various portfolio selection problems. However Markowitz's solution is only for a single period. Multi-period portfolio selection problems have been studied for a long time but most solutions depend on various forms of utility function, which are unfamiliar to general investors. Some works have formulated the problems as MV models and solved them analytically in closed form subject to certain assumptions. Unlike analytical solutions, genetic algorithms (GA) are more flexible because they can solve problems without restrictive assumptions. The purpose of this paper is to formulate multi-period portfolio selection problems as MV models and solve them by GA. To illustrate the generality of our algorithm, we implement a program by Microsoft Visual Studio to solve a multi-period portfolio selection problem for which there exists no general analytical solution.

Multi-period mean-variance portfolio selection with practical constraints using heuristic genetic algorithms

Since Markowitz proposed the mean-variance (MV) formulation in 1952, it has been used to configure various portfolio selection problems. However Markowitz's solution is only for a single period. Multi-period portfolio selection problems have been studied for a long time but most solutions depend on various forms of utility function, which are unfamiliar to general investors. Some works have formulated the problems as MV models and solved them analytically in closed form subject to certain assumptions. Unlike analytical solutions, genetic algorithms (GA) are more flexible because they can solve problems without restrictive assumptions. The purpose of this paper is to formulate multi-period portfolio selection problems as MV models and solve them by GA. To illustrate the generality of our algorithm, we implement a program by Microsoft Visual Studio to solve a multi-period portfolio selection problem for which there exists no general analytical solution.

Multi-period mean-variance portfolio selection in a regime-switching market with a bankruptcy state and a state-dependent uncertain exit-time

In this paper, we study optimal multi-period portfolio selection problem with uncertain exit-time under mean-variance criterion in a Markovian regime-switching market. The market state space contains an absorbing state which represents the bankruptcy state. It is assumed that all random key parameters, i.e., asset returns, the recovery rate, and the exit-time depend on the current market state. Three common mean-variance formulations are considered, i.e., minimum variance formulation, maximum expected return formulation and the trade-off formulation. First, the problem with an uncertain exit-time is reformulated as a problem with a certain exit-time. Then, by applying the Lagrange duality method and the dynamic programming approach, the optimal multi-period portfolio strategies and the efficient frontier are derived in a closed form. Moreover, the conditions under which the aforementioned three problems are (mutually) equivalent are given. A numerical example is provided to illustrate the results.