GAN-MP hybrid heuristic algorithm for non-convex portfolio optimization problem

Abstract

During recent decades, the traditional Markowitz model has been extended for asset cardinality, active share, and tracking-error constraints, which were introduced to overcome the drawbacks of the original Markowitz model. The resulting optimization problems, however, are often very difficult to solve, whereas those of the original Markowitz model are easily solvable. In order to resolve the portfolio optimization problem for the new extensions, we developed a novel heuristic algorithm that combines GAN (Generative Adversarial Networks) with mathematical programming: the GAN-MP hybrid heuristic algorithm. To the best of our knowledge, this is the first attempt to bridge neural networks (NN) and mathematical programming to tackle a real-world portfolio optimization problem. Computational experiments with real-life stock data show that our algorithm significantly outperforms the existing non-linear optimization solvers.     

Crypto-assets portfolio optimization under the omega measure

Abstract

Crypto-currencies, or crypto-assets, represent a new class of investment assets. The traditional portfolio analysis approach of Markowitz is not appropriate for use with portfolios containing crypto-assets, as the model requires that the investor have a quadratic utility function or that the returns be normally distributed, which isn’t the case for crypto-assets. We develop a portfolio optimization model based on the Omega measure which is more comprehensive than the Markowitz model, and apply this to four crypto-asset investment portfolios by means of a numerical application. The results indicate that these portfolios should favor traditional market assets over crypto-assets. In the case of portfolios formed only by crypto-assets, there is no clear preference in favor of any crypto-asset in particular.     

An extension to the classical mean–variance portfolio optimization model

Abstract

The purpose of this study is to find a portfolio that maximizes the risk-adjusted returns subject to constraints frequently faced during portfolio management by extending the classical Markowitz mean–variance portfolio optimization model. We propose a new two-step heuristic approach, GRASP & SOLVER, that evaluates the desirability of an asset by combining several properties about it into a single parameter. Using a real-life data set, we conduct a simulation study to compare our solution to a benchmark (S&P 500 index). We find that our method generates solutions satisfying nearly all of the constraints within reasonable computational time (under an hour), at the expense of a 13% reduction in the annual return of the portfolio, highlighting the effect of introducing these practice-based constraints.     

A Three-phase Approach to an Enhanced Index-tracking Problem with Real-life Constraints

Abstract

Enhanced index tracking is an emerging strategy for investing money in the stock market and is aimed at achieving outperformance over a given benchmark index while achieving a low tracking error. We consider the problem of rebalancing a portfolio for an enhanced index tracking strategy subject to various real-life constraints, including a lower bound and an upper bound on the expected tracking error. To solve this problem, we propose a three-phase approach consisting of preprocessing, optimization, and learning. In a computational experiment, we applied this approach to rebalance a given portfolio on a monthly basis over a time horizon of 10 years; the data for the S&P 500 benchmark index were provided by the investment company Principal Global Investors. Our approach generated portfolios that were provably close to optimality for all monthly rebalancing decisions. Over the entire horizon of 10 years, the portfolios devised by our approach yielded cumulative returns higher than the S&P 500 index after transaction costs with a moderate tracking error.     

Variable neighborhood search heuristic for nonconvex portfolio optimization

Abstract

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.     

An inexact l2-norm penalty method for cardinality constrained portfolio optimization

Abstract

We analyze and solve a single-period portfolio optimization problem with non-convex constraints, which address practical concerns of investment such as the active share weights of sectors and the number of stocks held in a portfolio. We reformulate the problem to simplify the computation and propose an inexact l₂-norm penalty method to solve the problem.     

Optimal Real Estate Portfolios

In recent years, increasing attention has been paid the problem of analyzing, evaluating and selecting real estate investments within the context of a portfolio. Most approaches simply attempt to adapt existing theory and models from the well-developed literature of securities investments. Most adaptations or extensions to real estate are not without serious problems, however, because of several fundamental difficulties relating to optimization technology inadequacies and a general lack of reliable and consistent market data.
This article deals with the major problems of utilizing some of the classic securities investment models for real estate. Further, a risk-return model is advanced which overcomes most of the fundamental problems outlined earlier in the article.     

Integrating Illiquid Assets into the Portfolio Decision Process

We consider the issues associated with modeling the decision to invest in an illiquid asset, such as real estate, over an extended period of time. Markets for illiquid assets tend to display certain characteristics: for example, significant time‐till‐sale and correlation in the rates of return over time. More importantly, as the liquidity of a market cannot be an issue if an investor never needs to liquidate an asset, we focus on how the liquidity of a market interacts with an individual's uncertain need to liquidate. We show that the optimal strategy is state contingent, if possible. We also show that the penalty associated with an illiquid investment depends on the characteristics of other assets being held in the portfolio, on the characteristics of liquidity shocks and on the interaction between time and behavior. We show that borrowing to pay for a liquidity shock cannot overcome all of the costs of owning an illiquid asset. In contrast, borrowing at t = 0 benefits from the complementarity in the assets. In a simpler model, we show that the portfolio perspective makes illiquid assets more valuable to an investor with a longer time horizon.     

Index fund optimization using a hybrid model: genetic algorithm and mixed-integer nonlinear programming

Abstract

Index funds consist of a subset of stocks, an index tracking portfolio, included in the market index. The index tracking portfolio aims to match the performance of the benchmark index. In this paper, we propose a hybrid model for solving the multiperiod index tracking problem, which includes rebalancing concerns, transaction costs, limits on the number of stocks, and diversification by sector, market capitalization, and stock weight. Our hybrid model combines the genetic algorithm (GA) to select stocks of the index tracking portfolio and mixed-integer nonlinear programming (MINLP) to estimate its weights. Finally, we apply our proposed hybrid model to the S&P500 to find an index tracking portfolio that includes those constraints. The results show that our hybrid model is able to create an index fund whose return rate is similar to the market index with significantly lower risk.     

Optimizing capital investments under technological change and deterioration: A case study on MRI machine replacement

ABSTRACT

We study the multiple style and type parallel asset replacement problem (MST-PRES), which determines an optimal policy for keeping or replacing a group of assets that operate in parallel under a limited budget. Operating assets generally suffer from deterioration, which results in high operation and maintenance (O&M) cost and decreased salvage value, and technological improvements make it possible for new assets to operate more efficiently at a lower cost. In order to address these issues, we formulate a multi-objective mixed-integer programming (MIP) model that minimizes fixed and variable costs of purchasing new assets, O&M cost, inventory cost, and penalty cost for unmet demand minus salvage values, while considering technological advances and deterioration as a gain and loss in capacity, respectively. We apply our model to a case study involving two different styles of assets: a full-body magnetic resonance imaging (MRI) machine and a smaller extremity magnetic resonance imaging (eMRI) machine. Each has two types: high-field and low-field. We perform computational experiments and analyses using key model parameters and illustrate optimal replacement strategies considering the impact of technological advances and deterioration. Results show that the proposed MIP model provides valuable insights and strategies for companies, decision makers, and government entities on the capital asset management.     

Product variety arising from hedging in the fashion supply chains

Consider a well-defined fashion apparel category, where the variants are distinguished by style and colour, and are subject to two equally likely states of the world: State1 when some variants become popular and others unpopular, and State2 when the reverse takes place. We analyse the optimal portfolio and variety arising from hedging against uncertainty triggered by the states, by integrating the Markowitz and the Newsboy models, while carefully considering demand correlations. We show that due to the complex structure of the uncertainty, building hedging portfolios with competing items is necessary for optimality. We also show how mis-specifying the distributions can lead to very bad trade-offs between risk and expected profit, caused by a lack of proper hedging.     

Complementary assets,start-ups and incentives to innovate

We examine to what extent market conditions facilitating start-up formation affect firms' R&D investment and profits. We consider a model in which R&D efforts of an incumbent firm generate partly tacit technological know-how embodied in a key R&D employee, who might use it to form a start-up. The availability of complementary assets influences whether new firms are created and determine expected profits for start-up's founders. A large availability of complementary assets has the direct effect that the generation of start-ups is fostered. However, as a strategic effect, the incentives of incumbents to invest in R&D may be reduced because of the increased danger of knowledge loss occurring through start-up formation. We characterize the effects of an increase in the availability of complementary assets, showing that counter-intuitively there are cases in which it induces an increase in incumbents' R&D investment.     

Game-theoretic modeling of pre-disaster relocation

Abstract

Sea-level rise due to climate change is clearly an important problem. This paper uses game theory in conjunction with discounting to explore strategies by which governments might encourage pre-disaster relocation by residents living in areas at high risk of flooding due to sea-level rise. We find that offering a subsidy (e.g., a partial buyout) can be effective if government has a significantly lower discount rate than residents. We also present extensions to our model, exploring the use of a fixed annual benefit after relocation (instead of a one-time subsidy), and hyperbolic instead of standard exponential discounting. Numerical sensitivity analysis elucidates many important factors affecting the timing of anticipatory relocation, since for example relocating too soon may be costly to both residents and government if flooding risk is increasing only gradually. This conceptual model also provides a foundation for future studies that quantify the model with more realistic parameter values (e.g., realistic estimates of flooding probabilities), and alternative behavioral models of resident decision making.     

Prioritizing Project Selection

We consider capital investments under uncertainty. A typical approach to this problem, when the problem parameters are assumed known, is via a multi-knapsack model. This model takes as input annual budgets as well as the cost streams and profit—i.e., net present value (NPV)—of each project. Its output is a portfolio of projects with the highest total NPV, observing yearly budget constraints. We argue that such a portfolio fails to hedge against uncertainties in the budgets, the cost streams, and the profits. As an alternative, we propose a model that forms an optimal priority list of projects, incorporating multiple scenarios for these input parameters. We apply our approach to two sets of example projects from the South Texas Project Nuclear Operating Company.     

Competition,governance, and relationship‐specific investments: Theory and implications for strategy

This paper uses biform games to examine the endogenous decision to invest in relationship‐specific assets. It addresses the questions of how competition affects suppliers' decisions to produce a general‐purpose product or a relationship‐specific product for a buyer and under what circumstances a governance arrangement designed to share investment costs between the transacting parties increases the investment in relationship‐specific assets. We offer a balanced perspective that emphasizes both the superior transaction value of relationship‐specific products and their high transaction costs while considering the competition effects generated by alternative investment plans. The model and its extensions generate new insights into investment decisions regarding relationship‐specific assets. Copyright © 2013 John Wiley & Sons, Ltd.     

Linear programming for bank portfolio management in Singapore

James Tobin's portfolio theory can be applied to bank portfolio management in that a bank would maximise the rates of return of its portfolio of assets, subject to the expected degree of risk and liquidity. Chambers and Charnes (1961), Cohen and Hammer (1967), Booth and Dash (1979) and others apply the linear programming model to the management of bank funds. This paper carries out a linear programming analysis on the consolidated balance sheets of commercial banks in Singapore for the period 1978–1983. The results show that by and large banks do try to maximise the returns of their portfolio, subject to legal, policy, bounding and total asset constraints, which denote riskiness and liquidity of the portfolio of assets. In a direct way, banks conform to the portfolio choice theory; they have to balance yield and liquidity against security. Although the computer cannot replace a manager, linear programming can serve as a useful guide.Dr Lee Sheng-Yi is an Associate Professor (retired) in the National University of Singapore and a Visiting Senior Research Fellow in Chung Hua Institution for Economic Research, Taipei; and Dr Yeong Wee Yong is a Senior Lecturer, School of Management Faculty of Business Administration, National University of Singapore.     

A Robust Optimization Approach to Capital Rationing and Capital Budgeting

We study the pure capital rationing and the horizon capital budgeting problems using a robust optimization framework. The models and the methodology we propose take into account the uncertainty of the input data. The uncertainty of the cash flows is modeled as a range of values that is allowed for each uncertain data. Unlike stochastic models, this approach does not make assumptions on the probability distribution of uncertain data. Moreover, this approach is highly tractable, easy to implement, and provides insights into portfolio selection problems. An attractive point of the model is that the decision maker can set the value of the parameters that control the robustness of the optimal solution, in order to balance the trade-off between protection level and performance. We illustrate our models with examples that show promising results. We also provide new duality and KKT optimality conditions.     

Revenue management for make-to-order manufacturing systems with a real-life application

Abstract

Due to successful applications of revenue management in the airline industry, in recent years, there has been a growing interest to adopt revenue management in make-to-order (MTO) manufacturing systems. Several interrelated decision problems such as order acceptance/rejection, short-term capacity planning, due date assignment, and order scheduling need to be studied simultaneously in order to manage revenues effectively in MTO manufacturing systems. Both the producer’s and customer’s requirements need to be taken into account through some negotiation mechanisms that are sensitive to the service-level reputation of the manufacturing companies. In this article, we propose a new dynamic bid price–based revenue management model that considers all of the aforementioned decision problems simultaneously. A simulation optimization approach is utilized in order to determine the best possible values of control parameters for bid price, due date assignment, and price increment/reduction mechanisms. The performance of the proposed integrated revenue management model is tested on both a hypothetical example and a real problem of a bridal gown company. The computational results show that the proposed model provides significant improvements in total revenue compared to other static and dynamic bid price policies.     

创业企业贷款组合风险管理研究——基于不同生命阶段的视角

投资品种的多样化与分散化是金融风险管理的核心方法,它可以有效地防范和控制各类风险。对银行业来说,将贷款分散地投放给不同行业、不同区域或处于不同生命阶段的企业,可以减少其因借款企业违约而可能遭受的损失。因此,银行在贷款投放过程中,如何进行多样化和分散化,以达到整个贷款组合收益的最大化和风险的最小化是一个决策难题。本文通过对贷款组合风险和预期收益的度量,提出针对不同生命阶段创业企业的贷款组合优化模型,并进行了相关实证研究,研究结果表明模型具有较强的适用性。     

Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.