Constrained Portfolio Selection Problem Research Articles

Product Supply Optimization for Crowdfunding Campaigns

Recent years have witnessed the rapid development of Finance Internet platforms, specifically, crowdfunding, which is for creators designing campaigns (projects) to collect funds from the public. Usually, the limited budget of a creator is manually divided into several perks (reward options), which should fit various market demand and further bring different monetary contributions for the campaign. Therefore, it is very challenging for each creator to design an effective allocation of perks when launching a campaign. Indeed, our aim is to enhance the funding performance of newly proposed campaigns, with a focus on optimizing the product supply of perks. In this paper, given the expected budget and the perks of a campaign, we propose a novel solution to automatically recommend the optimal product supply for balancing the expected return of this campaign against the risk. Along this line, we define it as a constrained portfolio selection problem, where the investment volume is measured by a multi-task learning method, and we adopt two kinds of methods for task splitting. Furthermore, we extend the investment volume prediction model with inner competition for capturing the competitive relationship between the perks in one campaign. Finally, extensive experiments on real-world crowdfunding data clearly prove the performance significantly.

Estimation of cardinality constrained portfolio efficiency via segmented DEA

The cardinality constrained portfolio selection problem arises due to the empirical findings that investors tend to hold a limited number of assets. Yet the lack of fast computational methods for frontier of cardinality constrained portfolio investments makes the performance evaluation of this problem a long-standing challenge. Classic Data Envelopment Analysis (DEA) models have been justified valid in evaluating and ranking portfolio performance. Unfortunately, when it comes to the cardinality constrained portfolio selection problem, the DEA models fail to approximate the portfolio efficiency (PE) since the real frontier is discontinuous and not concave. To solve this problem, we propose a segmented DEA approach based on data segment points. A searching algorithm is introduced to approach the real segment points and proved to be valid. In each segment, the frontier is continuous and concave; hence, classic DEA models can be applied to evaluate the PE. The simulation results further indicate that the segmented DEA approach proposed in this paper is effective and practical in evaluating the cardinality constrained portfolio performance.

Efficiency impact of convergence bidding in the california electricity market

The California Independent System Operator (CAISO) has implemented Convergence Bidding (CB) on February 1, 2011 under Federal Energy Regulatory Commission’s September 21, 2006 Market Redesign and Technology Upgrade Order. CB is a financial mechanism that allows market participants, including electricity suppliers, consumers and virtual traders, to arbitrage price differences between the day-ahead (DA) market and the real-time (RT) market without physically consuming or producing energy. In this paper, market efficiency is defined in terms of trading profitability, where a zero-profit competitive equilibrium implies market efficiency (Jensen in, J Financial Econ 6(2):95–101, 1978). We analyze market data in the CAISO electric power markets, and empirically test for market efficiency by assessing the performance of trading strategies from the perspective of virtual traders. By viewing DA–RT spreads as payoffs from a basket of correlated assets, we can formulate a chance constrained portfolio selection problem, where the chance constraint takes two different forms as a value-at-risk constraint and a conditional value-at-risk constraint, to find the optimal trading strategy. A hidden Markov model (HMM) is further proposed to capture the presence of the time-varying forward premium. This is meant to be a contribution to the modeling of regime shifts in the electricity forward premium with unobservable states. Our backtesting results cast doubt on the efficiency of the CAISO electric power markets, as the trading strategy generates consistent profits after the introduction of CB, even in the presence of transaction costs. Nevertheless, by comparing with the performance before the introduction of CB, we find that the profitability decreases significantly, which enables us to identify the efficiency gain brought about by CB. Convincing evidence for the improvement of market efficiency in the presence of CB is further provided by the test for the Bessembinder and Lemmon (J Finance 57(3):1347–1382, 2002) model.

Portfolio Selection with Multiple Spectral Risk Constraints

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value-at-risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.

A hybrid algorithm for constrained portfolio selection problems

Since Markowitz's seminal work on the mean-variance model in modern portfolio theory, many studies have been conducted on computational techniques and recently meta-heuristics for portfolio selection problems. In this work, we propose and investigate a new hybrid algorithm integrating the population based incremental learning and differential evolution algorithms for the portfolio selection problem. We consider the extended mean-variance model with practical trading constraints including the cardinality, floor and ceiling constraints. The proposed hybrid algorithm adopts a partially guided mutation and an elitist strategy to promote the quality of solution. The performance of the proposed hybrid algorithm has been evaluated on the extended benchmark datasets in the OR Library. The computational results demonstrate that the proposed hybrid algorithm is not only effective but also efficient in solving the mean-variance model with real world constraints.

Portfolio Selection with Multiple Spectral Risk Constraints

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.

Hybrid metaheuristics for constrained portfolio selection problems

Portfolio selection is a problem arising in finance and economics. While its basic formulations can be efficiently solved using linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cases to be tackled by heuristics. In this work, we present a hybrid technique that combines a local search metaheuristic, as master solver, with a quadratic programming procedure, as slave solver. Experimental results show that the approach is very promising, as it regularly provides the optimal solution and thus achieves results comparable, or superior, to state-of-the-art solvers, including widespread commercial software tools (CPLEX 11.0.1 and MOSEK 5). The paper reports a detailed analysis of the behavior of the technique in various constraint settings, thus demonstrating how the performance is dependent on the features of the instance.

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the e-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.

A new particle swarm optimisation based on MATLAB for portfolio selection problem

This paper focuses on the constrained portfolio selection problem and develops an improved particle swarm optimisation (IPSO) algorithm to solve it. As an alternative and extension to the standard Markowitz model, a constrained portfolio selection model with transaction costs and quantity limit is formulated for selecting portfolios. Due to these complex constraints, the process becomes a high-dimensional constrained optimisation problem. Traditional optimisation algorithms fail to work efficiently and heuristic algorithms with effective searching ability can be the best choice for the problem, so we design an IPSO to solve our problem. In order to prevent premature convergence to local minima, we design a new definition for global point. Finally, a numerical example of a portfolio selection problem is given to illustrate our proposed method; the simulation results demonstrate good performance of the IPSO in solving the complex constrained portfolio selection problem.