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Although the modern portfolio theory (MPT) asset allocation framework can be adopted to enable decision making for international and direct real estate investing, and that many institutional investors adopt it to support their decision making, this framework can be enhanced to capture the multi‐causal factors influencing international and direct real estate investing. The purpose of this paper is to explain how a fuzzy decision‐making approach is a more intuitive, yet rigorous alternative in this regard.

This paper is concerned with the model formation and estimation of a unique fuzzy tactical asset allocation (FTAA), which in turn comprises the FTAA flexible programming model and the FTAA robust programming model.

Both these FTAA models enhance the classical, Markowitz MPT portfolio theory on asset allocation through making it more intuitively appropriate for decision making in international and direct real estate investing.

These two FTAA models achieve the benefits of intuitively greater risk diversification by city or real estate sector and enable effective risk management. These two short‐run fuzzy models would be accepted and more such models would emerge as an effective extension of quadratic programming optimization, as more computable software programs of this kind are widespread.

Fuzzy approaches to asset allocation in the short run, are limited by some drawbacks. Fuzzy models possess the common feature of converting the equality function under quadratic programming optimization into inequality functions. Such inequality optimization replaces the point solution of the MPT TAA optimization problem, obtained through the rigid intersection of all functions, via a generalized or intuitive answer over a defined space of alternatives. The product of the fuzzy process with fuzzy inputs, in the form of fuzzy outcome is in actual fact a more natural and intuitive approach to asset optimization.

This chapter presents the portfolio optimization problem formulated as a multi-criteria mixed integer program. Weighting and lexicographic approach are proposed. The portfolio selection problem considered is based on a single-period model of investment. An extension of the Markowitz portfolio optimization model is considered, in which the variance has been replaced with the Value-at-Risk (VaR). The VaR is a quantile of the return distribution function. In the classical Markowitz approach, future returns are random variables controlled by such parameters as the portfolio efficiency, which is measured by the expectation, whereas risk is calculated by the standard deviation. As a result, the classical problem is formulated as a quadratic program with continuous variables and some side constraints. The objective of the problem considered in this chapter is to allocate wealth on different securities to maximize the weighted difference of the portfolio expected return and the threshold of the probability that the return is less than a required level. The auxiliary objectives are minimization of risk probability of portfolio loss and minimization of the number of security types in portfolio. The four types of decision variables are introduced in the model: a continuous wealth allocation variable that represents the percentage of wealth allocated to each asset, a continuous variable that prevents the probability that return of investment is not less than required level, a binary selection variable that prevents the choice of portfolios whose VaR is below the minimized threshold, and a binary selection variable that represents choice of stocks in which capital should be invested. The results of some computational experiments with the mixed integer programming approach modeled on a real data from the Warsaw Stock Exchange are reported.

Standard market risk optimization tools, based on assumptions of normality, are ineffective for evaluating credit risk. In this article, the authors develop three scenario optimization models for portfolio credit risk. They first create the trading risk profile and find the best hedge position for a single asset or obligor. The second model adjusts all positions simultaneously to minimize the regret of the portfolio subject to general linear restrictions. Finally, a credit risk‐return efficient frontier is constructed using parametric programming. While scenario optimization of quantile‐based credit risk measures leads to problems that are not generally tractable, regret is a relevant and tractable measure that can be optimized using linear programming. The three models are applied to optimizing the risk‐return profile of a portfolio of emerging market bonds.

Optimization of energy planning for growth and sustainable development has become very important in the context of climate change mitigation imperatives in developing countries. Existing models do not capture developing country realities adequately. The purpose of this paper is to conceptualizes a framework for energy strategy optimization of the Indian energy sector, which can be applied in all emerging economies.

Hierarchical multi‐objective policy optimization methodology adopts a policy‐centric approach and groups the energy strategies into multi‐level portfolios based on convergence of objectives appropriate to each level. This arrangement facilitates application of the optimality principle of dynamic programming. Synchronised optimization of strategies with respect to the common objectives at each level results in optimal policy portfolios.

The reductionist policy‐centric approach to complex energy economy modelling, facilitated by the dynamic programming methodology, is most suitable for policy optimization in the context of a developing country. Barriers to project implementation and cost risks are critical features of developing countries which are captured in the framework in the form of a comprehensive risk barrier index. Genetic algorithms are suitable for optimization of the first level objectives, while the efficiency approach, using restricted weight stochastic data envelopment analysis, is appropriate for higher levels of the objective hierarchy.

The methodology has been designed for application to the energy sector planning for India's 12th Five Year Plan for which the objectives of faster growth, better inclusion, energy security and sustainability have been identified. The conceptual framework combines, within the policy domain, the bottom‐up and top‐down processes to form a hybrid modelling approach yielding optimal outcomes, transparent and convincing to the policy makers. The research findings have substantial implications for transition management to a sustainable energy framework.

The methodology is general in nature and can be employed in all sectors of the economy. It is especially suited to policy design in developing countries with the ground realities factored into the model as project barriers. It offers modularity and flexibility in implementation and can accommodate all the key strategies from diverse sectors along with multiple objectives in the policy optimization process. It enables adoption of an evidence‐based and transparent approach to policy making. The research findings have substantial value for transition management to a sustainable energy framework in developing countries.

This paper aims to examine from commodity portfolio managers’ perspective the performance of liquidity adjusted risk modeling in assessing the market risk parameters of a large commodity portfolio and in obtaining efficient and coherent portfolios under different market circumstances.

The implemented market risk modeling algorithm and investment portfolio analytics using reinforcement machine learning techniques can simultaneously handle risk-return characteristics of commodity investments under regular and crisis market settings besides considering the particular effects of the time-varying liquidity constraints of the multiple-asset commodity portfolios.

In particular, the paper implements a robust machine learning method to commodity optimal portfolio selection and within a liquidity-adjusted value-at-risk (LVaR) framework. In addition, the paper explains how the adapted LVaR modeling algorithms can be used by a commodity trading unit in a dynamic asset allocation framework for estimating risk exposure, assessing risk reduction alternates and creating efficient and coherent market portfolios.

The optimization parameters subject to meaningful operational and financial constraints, investment portfolio analytics and empirical results can have important practical uses and applications for commodity portfolio managers particularly in the wake of the 2007–2009 global financial crisis. In addition, the recommended reinforcement machine learning optimization algorithms can aid in solving some real-world dilemmas under stressed and adverse market conditions (e.g. illiquidity, switching in correlations factors signs, nonlinear and non-normal distribution of assets’ returns) and can have key applications in machine learning, expert systems, smart financial functions, internet of things (IoT) and financial technology (FinTech) in big data ecosystems.

This chapter presents selected multiobjective methods for multiperiod portfolio optimization problem. Portfolio models are formulated as multicriteria mixed integer programs. Reference point method together with weighting approach is proposed. The portfolio selection problem considered is based on a multiperiod model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to allocate the wealth on different securities to optimize the portfolio expected return, the probability that the return is not less than a required level. Multiobjective methods were used to find tradeoffs between risk, return, and the number of securities in the portfolio. In computational experiments the data set of daily quotations from the Warsaw Stock Exchange were used.

The principal concern of organization managers in the global rivalry of commerce environment is how to select the project portfolio among available projects. In this matter, organizations should consider the uncertainty intrinsic in the projects regarding an appropriate valuation technique within an optimization framework. In this research, the purpose of this paper is to formulate using a robust optimization algorithm to deal with the complexities and uncertainty inherent in the construction of the project portfolio.

First, a general mathematical formulation is presented, which in compound real options valuation is highlighted. This formulation gives managerial flexibility by correcting the deficiency of traditional discounted cash flow technique that excludes any form of flexibility. Then, considering a limitation on budget of the organization, an integer programming formulation to maximize the n-fold compound options for project portfolio selection is proposed. Finally, a robust optimization model is developed along with the robust combinatorial optimization algorithm, which is effective for solving problems under uncertainty.

Sensitivity analysis showed that projects in later phases of development, having survived several phases of pre-clinical and clinical tests, are worth more because they are more likely to pertain to business. However, the investment costs related to each project during development phases limit the number of projects that a company can bring to their final portfolio. Additionally, the analysis of conservatism level represented how project managers can quite easily determine their risk attitude and the corresponding portfolio composition. From a managerial point of view, the proposed framework is very useful because it requires only financial estimates. Hence, the proposed decision support tool can assist research and development (R&D) project managers in the pharmaceutical industry for making decisions.

The first is the application of the n-fold compound options on portfolio of R&D projects and the employment of compound options value of a project portfolio as an objective function. The second one is a mathematical formulation of these concepts and solving it by the robust combinatorial optimization algorithm. The literature is lacking in the application of the robust combinatorial optimization algorithm to R&D project portfolio selection based on the generalized n-fold compound option model of Cassimon et al. (2004). Every framework from calculation of the n-fold compound option to solving robust combinatorial algorithm is programmed in Matlab software, since it can be used as a business support tool.

This study aims to examine the theoretical foundations for multivariate portfolio optimization algorithms under illiquid market conditions. In this study, special emphasis is devoted to the application of a risk-engine, which is based on the contemporary concept of liquidity-adjusted value-at-risk (LVaR), to multivariate optimization of investment portfolios.

This paper examines the modeling parameters of LVaR technique under event market settings and discusses how to integrate asset liquidity risk into LVaR models. Finally, the authors discuss scenario optimization algorithms for the assessment of structured investment portfolios and present a detailed operational methodology for computer programming purposes and prospective research design with the backing of a graphical flowchart.

To that end, the portfolio/risk manager can specify different closeout horizons and dependence measures and calculate the necessary LVaR and resulting investable portfolios. In addition, portfolio managers can compare the return/risk ratio and asset allocation of obtained investable portfolios with different liquidation horizons in relation to the conventional Markowitz´s mean-variance approach.

The examined optimization algorithms and modeling techniques have important practical applications for portfolio management and risk assessment, and can have many uses within machine learning and artificial intelligence, expert systems and smart financial applications, financial technology (FinTech), and within big data environments. In addition, it provide key real-world implications for portfolio/risk managers, treasury directors, risk management executives, policymakers and financial regulators to comply with the requirements of Basel III best practices on liquidly risk.

The proposed optimization algorithms can aid in advancing portfolios selection and management in financial markets by assessing investable portfolios subject to meaningful operational and financial constraints. Furthermore, the robust risk-algorithms and portfolio optimization techniques can aid in solving some real-world dilemmas under stressed and adverse market conditions, such as the effect of liquidity when it dries up in financial and commodity markets, the impact of correlations factors when there is a switching in their signs and the integration of the influence of the nonlinear and non-normal distribution of assets’ returns in portfolio optimization and management.

Supply chain is an important aspect for all the companies and can affect many aspects of companies. Especially the disruption in supply chain is causing huge impacts and consequences that are difficult to deal with. This chapter presents a review of selected multiple criteria problems used in supply chain optimization. Research analyzed the multiple criteria decision-making methods to tackle the problem of supplier evaluation and selection. It also focuses on the problem of supply chain when a disruption happens and presents strategies to deal with the issue of disruptions in supply chain and how to mitigate the impact of disruptions. Prevention, response, protection, and recovery strategies are explained. Practical part is focused in the risk-averse models to minimize expected worst-case scenario by single sourcing. Computational experiments for practical examples have been solved using CPLEX solver.

To solve the multi‐period portfolio management problem under transactions costs.

We apply a recently designed super genetic hybrid algorithm (SuperGHA) – an integrated optimisation system for simultaneous parametric search and non‐linear optimisation – to a recursive portfolio management decision support system (SHAREX). The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimisation process.

SHAREX seems to outperform the buy and hold‐strategy on the Finnish stock market. The potential of a technical portfolio system is best exploitable under favorable market conditions.

A number of robust engines for matrix algebra, mathematical programming and numerical calculus have been integrated with SuperGHA. The engines expand its scope as a general‐purpose algorithm for mathematical programming.