Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic

In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the expected variance, so-called Expected Mean-Variance. The model is formulated as a multistage stochastic mixed-integer quadratic programming problem combining risk-sensitive cost and scenario analysis approaches. The proposed problem is solved by a matheuristic based on the Branch-and-Fix Coordination method. The multistage scenario cluster primal decomposition framework is extended to deal with large-scale quadratic optimization by means of stage-wise reformulation techniques. A specific case study in risk-sensitive production planning is used to illustrate that a remarkable decrease in the expected variance (risk cost) is obtained. A competitive behavior on the part of our methodology in terms of solution quality and computation time is shown when comparing with plain use of CPLEX in 150 benchmark instances, ranging up to 711,845 constraints and 193,000 binary variables.project MTM2015-65317-P (MINECO/FEDER/EU); BERC 2014-2017; IT-928-16; and by the University of the Basque Country UPV/EHU; BCAM Severo Ochoa excellence accreditation Grant SEV-2013-0323; BERC 2014-201

Tax effects on investments

This doctoral thesis investigates empirically and theoretically the effect of tax on the composition of the optimal allocation of wealth to risky assets from various points of view. The first empirical chapter considers the effect of tax on a U.K. personal investor targeting domestic financial products. This research helps investors estimate the impact of a future tax change and maximize their portfolio return using a newly proposed optimization model and solution method. Following Bonami and Lejeune (2009), personal portfolios are constrained to meet or exceed a prescribed return threshold with a high confidence level and satisfy buy-in threshold and diversification constraints. Their model is improved by incorporating complex tax trading rules with withdrawal features that enhance those considered by Osorio et al. (2004, 2008). A solution based on Greedy methods is developed to deal with the proposed large-scale portfolio optimization problem. The empirical results report substantial non-linear tax effects on riskier assets and enhanced effects of withdrawal tax only when tax rates are high. The developed framework better enables investors to react to tax changes, and tax policy makers to quantify the influence of tax changes on private investment preferences. The second empirical chapter investigates the effect of an international transaction tax, the so-called ‘Tobin tax’, from the point of view of U.K., U.S., and E.U. personal investors targeting international financial products. This empirical research helps the policy maker to estimate the impact of Tobin tax on international capital flows and, therefore, assess the optimal way to introduce the new tax. An optimization model is proposed to maximize the expected net Sharpe ratio and find the optimal risky portfolio internationally. Complex trading and tax rules are considered. To examine the precise effects of different investment and transaction tax rules, a comparison of four tax settings is presented: source only, residence only, mixed with credit and mixed with double taxation. The experimental results show that a source only tax union has more capital transits in international markets than a residence only tax union, and its optimal market portfolio is more sensitive to regional tax policy. In a mixed tax system, double taxation between residence- and source-taxed markets significantly reduces the attraction of the latter while its attraction is maintained with the credit method. Tobin tax can reduce the volatility of the market but the effect varies with tax rate, certain market specifications (e.g., expected returns and correlations with overseas markets) and investment tax rules. It does not depend on which side of the capital flow (inflow or outflow) is subject to Tobin tax. Finally, an agreement among countries to produce a consistent Tobin tax rate globally can significantly reduce the negative effect of Tobin tax on capital flows while retaining its positive effect on market stability in comparison to heterogeneous Tobin tax rates. Finally, the third analytical chapter investigates theoretically the effect of tax from the point of view of an arbitrageur. This theoretical research addresses the condition of the existence of arbitrage opportunities on an after-tax basis, helping the policy maker improve the fairness and efficiency of markets by addressing effective tax policy. To track tax arbitrage, continuous time optimization models are developed with heterogeneous taxation between investors programmed with continuous rather than static income and capital gains (or losses). It is proved analytically that arbitrage opportunities exist for both perfectly correlated and non-perfectly correlated assets. For perfectly correlated assets, the analysis shows that tax arbitrage may exist, with the investor’s top tax rate and some static asset parameters determining the existence of arbitrage opportunities. It is also proved that many of the equilibria obtained under income tax only are not optimal if investors are also subject to capital gains tax. For non-perfectly correlated assets, however, it is the market prices of cap and floor options on asset returns that decide the existence of tax arbitrage. In the government fixed income bond market, tax arbitrage between investors is difficult to eliminate unless investors are all subject to the same tax rates. But the return from this arbitrage can be limited if the government applies the same top tax rate to all investors

A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption

Supply chain network design under uncertainty and risk

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We consider the research problem of quantitative support for decision making in supply chain network design (SCND). We first identify the requirements for a comprehensive SCND as (i) a methodology to select uncertainties, (ii) a stochastic optimisation model, and (iii) an appropriate solution algorithm. We propose a process to select a manageable number of uncertainties to be included in a stochastic program for SCND. We develop a comprehensive two-stage stochastic program for SCND that includes uncertainty in demand, currency exchange rates, labour costs, productivity, supplier costs, and transport costs. Also, we consider conditional value at risk (CV@R) to explore the trade-off between risk and return. We use a scenario generator based on moment matching to represent the multivariate uncertainty. The resulting stochastic integer program is computationally challenging and we propose a novel iterative solution algorithm called adaptive scenario refinement (ASR) to process the problem. We describe the rationale underlying ASR, validate it for a set of benchmark problems, and discuss the benefits of the algorithm applied to our SCND problem. Finally, we demonstrate the benefits of the proposed model in a case study and show that multiple sources of uncertainty and risk are important to consider in the SCND. Whereas in the literature most research is on demand uncertainty, our study suggests that exchange rate uncertainty is more important for the choice of optimal supply chain strategies in international production networks. The SCND model and the use of the coherent downside risk measure in the stochastic program are innovative and novel; these and the ASR solution algorithm taken together make contributions to knowledge

Employees Provident Fund (EPF) Malaysia: Generic models for asset and liability management under uncertainty

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We describe Employees Provident Funds (EPF) Malaysia. We explain about Defined Contribution and Defined Benefit Pension Funds and examine their similarities and differences. We also briefly discuss and compare EPF schemes in four Commonwealth countries. A family of Stochastic Programming Models is developed for the Employees Provident Fund Malaysia. This is a family of ex-ante decision models whose main aim is to manage, that is, balance assets and liabilities. The decision models comprise Expected Value Linear Programming, Two Stage Stochastic Programming with recourse, Chance Constrained Programming and Integrated Chance Constraints Programming. For the last three decision models we use scenario generators which capture the uncertainties of asset returns, salary contributions and lump sum liabilities payments. These scenario generation models for Assets and liabilities were developed and calibrated using historical data. The resulting decisions are evaluated with in-sample analysis using typical risk adjusted performance measures. Out- of- sample testing is also carried out with a larger set of generated scenarios. The benefits of two stage stochastic programming over deterministic approaches on asset allocation as well as the amount of borrowing needed for each pre-specified growth dividend are demonstrated. The contributions of this thesis are i) an insightful overview of EPF ii) construction of scenarios for assets returns and liabilities with different values of growth dividend, that combine the Markov population model with the salary growth model and retirement payments iii) construction and analysis of generic ex-ante decision models taking into consideration uncertain asset returns and uncertain liabilities iv) testing and performance evaluation of these decisions in an ex-post setting.This stuyd is funded by the Universiti Teknologi MARA Malaysia

Economic and regulatory uncertainty in renewable energy system design: a review

Renewable energy is increasingly mobilizing more investment around the globe. However, there has been little attention to evaluating economic and regulatory (E&R) uncertainties, despite their enormous impact on the project cashflows. Consequently, this review analyzes, classifies, and discusses 130 articles dealing with the design of renewable energy projects under E&R uncertainties. After performing a survey and identifying the selected manuscripts, and the few previous reviews on the matter, the following innovative categorization is designed: sources of uncertainty, uncertainty characterization methods, problem formulations, solution methods, and regulatory frameworks. The classification reveals that electricity price is the most considered source of uncertainty, often alone, despite the existence of six other equally influential groups of E&R uncertainties. In addition, real options and optimization arise as the two main approaches researchers use to solve problems in energy system design. Subsequently, the following aspects of interest are discussed in depth: how modeling can be improved, which are the most influential variables, and potential lines of research. Conclusions show the necessity of modeling E&R uncertainties with currently underrepresented methods, suggest several policy recommendations, and encourage the integration of prevailing approaches.Peer ReviewedObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No Contaminant::7.2 - Per a 2030, augmentar substancialment el percentatge d’energia renovable en el con­junt de fonts d’energiaObjectius de Desenvolupament Sostenible::7 - Energia Assequible i No ContaminantPostprint (published version

Measuring the variability in supply chains with the peakedness

This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects.variability, peakedness, supply chain

Joined-Up Pensions Policy in the UK: An Asset-Libility Model for Simultaneously Determining the Asset Allocation and Contribution Rate

The trustees of funded defined benefit pension schemes must make two vital and inter-related decisions - setting the asset allocation and the contribution rate. While these decisions are usually taken separately, it is argued that they are intimately related and should be taken jointly. The objective of funded pension schemes is taken to be the minimization of both the mean and the variance of the contribution rate, where the asset allocation decision is designed to achieve this objective. This is done by splitting the problem into two main steps. First, the Markowitz mean-variance model is generalised to include three types of pension scheme liabilities (actives, deferreds and pensioners), and this model is used to generate the efficient set of asset allocations. Second, for each point on the risk-return efficient set of the asset-liability portfolio model, the mathematical model of Haberman (1992) is used to compute the corresponding mean and variance of the contribution rate and funding ratio. Since the Haberman model assumes that the discount rate for computing the present value of liabilities equals the investment return, it is generalised to avoid this restriction. This generalisation removes the trade-off between contribution rate risk and funding ratio risk for a fixed spread period. Pension schemes need to choose a spread period, and it is shown how this can be set to minimise the variance of the contribution rate. Finally, using the result that the funding ratio follows an inverted gamma distribution, shortfall risk and expected tail loss are computed for funding below the minimum funding requirement, and funding above the taxation limit. This model is then applied to one of the largest UK pension schemes - the Universities Superannuation Scheme