Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

Robust optimisation and its application to portfolio planning

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Decision making under uncertainty presents major challenges from both modelling and solution methods perspectives. The need for stochastic optimisation methods is widely recognised; however, compromises typically have to be made in order to develop computationally tractable models. Robust optimisation is a practical alternative to stochastic optimisation approaches, particularly suited for problems in which parameter values are unknown and variable. In this thesis, we review robust optimisation, in which parameter uncertainty is defined by budgeted polyhedral uncertainty sets as opposed to ellipsoidal sets, and consider its application to portfolio selection. The modelling of parameter uncertainty within a robust optimisation framework, in terms of structure and scale, and the use of uncertainty sets is examined in detail. We investigate the effect of different definitions of the bounds on the uncertainty sets. An interpretation of the robust counterpart from a min-max perspective, as applied to portfolio selection, is given. We propose an extension of the robust portfolio selection model, which includes a buy-in threshold and an upper limit on cardinality. We investigate the application of robust optimisation to portfolio selection through an extensive empirical investigation of cost, robustness and performance with respect to risk-adjusted return measures and worst case portfolio returns. We present new insights into modelling uncertainty and the properties of robust optimal decisions and model parameters. Our experimental results, in the application of portfolio selection, show that robust solutions come at a cost, but in exchange for a guaranteed probability of optimality on the objective function value, significantly greater achieved robustness, and generally better realisations under worst case scenarios

Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails

Slow Adaptive OFDMA Systems Through Chance Constrained Programming

Adaptive OFDMA has recently been recognized as a promising technique for providing high spectral efficiency in future broadband wireless systems. The research over the last decade on adaptive OFDMA systems has focused on adapting the allocation of radio resources, such as subcarriers and power, to the instantaneous channel conditions of all users. However, such "fast" adaptation requires high computational complexity and excessive signaling overhead. This hinders the deployment of adaptive OFDMA systems worldwide. This paper proposes a slow adaptive OFDMA scheme, in which the subcarrier allocation is updated on a much slower timescale than that of the fluctuation of instantaneous channel conditions. Meanwhile, the data rate requirements of individual users are accommodated on the fast timescale with high probability, thereby meeting the requirements except occasional outage. Such an objective has a natural chance constrained programming formulation, which is known to be intractable. To circumvent this difficulty, we formulate safe tractable constraints for the problem based on recent advances in chance constrained programming. We then develop a polynomial-time algorithm for computing an optimal solution to the reformulated problem. Our results show that the proposed slow adaptation scheme drastically reduces both computational cost and control signaling overhead when compared with the conventional fast adaptive OFDMA. Our work can be viewed as an initial attempt to apply the chance constrained programming methodology to wireless system designs. Given that most wireless systems can tolerate an occasional dip in the quality of service, we hope that the proposed methodology will find further applications in wireless communications

A superior active portfolio optimization model for stock exchange

Due to the vast number of stocks and the multiple appearances of developing investment portfolios, investors in the financial market face multiple investment opportunities. In this regard, the investor task becomes extremely difficult as investors define their preferences for expected return and the amount to which they want to avoid potential investment risks. This research attempts to design active portfolios that outperform the performance of the appropriate market index. To achieve this aim, technical analysis and optimization procedures were used based on a hybrid model. It combines the strong features of the Markowitz model with the General Reduced Gradient (GRG) algorithm to maintain a good compromise between diversification and exploitation. The proposed model is used to construct an active portfolio optimization model for the Iraq Stock Exchange (ISX) for the period from January 2010 to February 2020. This is applied to all 132 companies registered on the exchange. In addition to the market portfolio, two methods, namely, Equal Weight (EW) and Markowitz were used to generate active portfolios to compare the research findings. After a thorough review based on the Sharpe ratio criterion, the suggested model demonstrated its robustness, resulting in maximizing earnings with low risks

Robust and Multi-objective Portfolio Selection

In this thesis, robust and multi-objective portfolio selection problem will be studied. New models and computational algorithms will be developed to solve the proposed models. In particularly, we have studied multi-objective portfolio selection with inexact information on investment return and covariance matrix. The problems have been transformed into easily solvable problems through theoretical analysis. Numerical experiments are presented to validate the methods

Distributionally robust optimization with applications to risk management

Many decision problems can be formulated as mathematical optimization models. While deterministic optimization problems include only known parameters, real-life decision problems almost invariably involve parameters that are subject to uncertainty. Failure to take this uncertainty under consideration may yield decisions which can lead to unexpected or even catastrophic results if certain scenarios are realized. While stochastic programming is a sound approach to decision making under uncertainty, it assumes that the decision maker has complete knowledge about the probability distribution that governs the uncertain parameters. This assumption is usually unjustified as, for most realistic problems, the probability distribution must be estimated from historical data and is therefore itself uncertain. Failure to take this distributional modeling risk into account can result in unduly optimistic risk assessment and suboptimal decisions. Furthermore, for most distributions, stochastic programs involving chance constraints cannot be solved using polynomial-time algorithms. In contrast to stochastic programming, distributionally robust optimization explicitly accounts for distributional uncertainty. In this framework, it is assumed that the decision maker has access to only partial distributional information, such as the first- and second-order moments as well as the support. Subsequently, the problem is solved under the worst-case distribution that complies with this partial information. This worst-case approach effectively immunizes the problem against distributional modeling risk. The objective of this thesis is to investigate how robust optimization techniques can be used for quantitative risk management. In particular, we study how the risk of large-scale derivative portfolios can be computed as well as minimized, while making minimal assumptions about the probability distribution of the underlying asset returns. Our interest in derivative portfolios stems from the fact that careless investment in derivatives can yield large losses or even bankruptcy. We show that by employing robust optimization techniques we are able to capture the substantial risks involved in derivative investments. Furthermore, we investigate how distributionally robust chance constrained programs can be reformulated or approximated as tractable optimization problems. Throughout the thesis, we aim to derive tractable models that are scalable to industrial-size problems