A compromise based fuzzy goal programming approach with satisfaction function for multi-objective portfolio optimisation

In this paper we investigate a multi-objective portfolio selection model with three criteria: risk, return and liquidity for investors. Non-probabilistic uncertainty factors in the market, such as imprecision and vagueness of investors’ preference and judgement are simulated in the portfolio selection process. The liquidity of portfolio cannot be accurately predicted in the market, and thus is measured by fuzzy set theory. Invertors’ individual preference and judgement are cooperated in the decision making process by using satisfaction functions to measure the objectives. A compromise based goal programming approach is applied to find compromised solutions. By this approach, not only can we obtain quality solutions in a reasonable computational time, but also we can achieve a trade-off between the objectives according to investors’ preference and judgement to enable a better decision making. We analyse the portfolio strategies obtained by using the proposed simulation approach subject to different settings in the satisfaction functions

A Polynomial Optimization Approach to Constant Rebalanced Portfolio Selection

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.Multi-period portfolio optimization;Polynomial optimization problem;Constant rebalancing;Semidefinite programming;Mean-variance criterion

Optimizing Strategic Allocation of Vehicles for One-Way Car-sharing Systems Under Demand Uncertainty

Car-sharing offers an environmentally sustainable, socially responsible and economically feasible mobility form in which a fleet of shared-use vehicles in a number of locations can be accessed and used by many people on as-needed basis at an hourly or mileage rate. To ensure its sustainability, car-sharing operators must be able to effectively manage dynamic and uncertain demands, and make the best decisions on strategic vehicle allocation and operational vehicle reallocation both in time and space to improve their profits while keeping costs under control. This paper develops a stochastic optimization method to optimize strategic allocation of vehicles for one-way car-sharing systems under demand uncertainty. A multi-stage stochastic linear programming model is developed and solved for use in the context of car-sharing. A seven-stage experimental network study is conducted. Numerical results and computational insights are discussed

A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty. To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed

A stochastic program for optimizing military sealift subject to attack

We describe a stochastic program for planning the wartime, sealift deployment of military cargo subject to attack. The cargo moves on ships from US or allied seaports of embarkation through seaports of debarkation (SPODs) near the theater of war where it is unloaded and sent on to final , in-theater destinations. The question we ask is: Can a deployment-planning model, with probabilistic knowledge of the time and location of potential enemy attacks on SPODs, successfully hedge against those attacks? That is, can this knowledge be used to reduce the expected disruption caused by such attacks? A specialized, multi-stage stochastic mixed-integer program is developed and answers that question in the affirmative. Furthermore, little penalty is incurred with the stochastic solution when no attack occurs, and worst-case scenarios are better. In the short term, insight gained from the stochastic-programming approach also enables better scheduling using current rule-based methods

Risk Aversion and CO2 Regulatory Uncertainty in Power Generation Investment: Policy and Modeling Implications

Our simulation considers producers in a competitive energy market. Risk averse producers face uncertainty about future carbon regulation. Investment decisions are a two-stage equilibrium problem. Initially, investment is made under regulatory uncertainty; then the regulatory state is revealed and producers realize returns. We consider taxes, grandfathered permits and auctioned permits and show that outcomes vary under risk aversion; some anticipated policies yield perverse investment incentives, in that investment in the dirty technology is encouraged. Beliefs about the policy instrument that will be used to price carbon may be as important as certainty that carbon will be priced. More generally, a failure to consider risk aversion may bias policy models of the power sector

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

Essays on Multistage Stochastic Programming applied to Asset Liability Management

Uncertainty is a key element of reality. Thus, it becomes natural that the search for methods allows us to represent the unknown in mathematical terms. These problems originate a large class of probabilistic programs recognized as stochastic programming models. They are more realistic than deterministic ones, and their aim is to incorporate uncertainty into their definitions. This dissertation approaches the probabilistic problem class of multistage stochastic problems with chance constraints and joint-chance constraints. Initially, we propose a multistage stochastic asset liability management (ALM) model for a Brazilian pension fund industry. Our model is formalized in compliance with the Brazilian laws and policies. Next, given the relevance of the input parameters for these optimization models, we turn our attention to different sampling models, which compose the discretization process of these stochastic models. We check how these different sampling methodologies impact on the final solution and the portfolio allocation, outlining good options for ALM models. Finally, we propose a framework for the scenario-tree generation and optimization of multistage stochastic programming problems. Relying on the Knuth transform, we generate the scenario trees, taking advantage of the left-child, right-sibling representation, which makes the simulation more efficient in terms of time and the number of scenarios. We also formalize an ALM model reformulation based on implicit extensive form for the optimization model. This technique is designed by the definition of a filtration process with bundles, and coded with the support of an algebraic modeling language. The efficiency of this methodology is tested in a multistage stochastic ALM model with joint-chance constraints. Our framework makes it possible to reach the optimal solution for trees with a reasonable number of scenarios.A incerteza é um elemento fundamental da realidade. Então, torna-se natural a busca por métodos que nos permitam representar o desconhecido em termos matemáticos. Esses problemas originam uma grande classe de programas probabilísticos reconhecidos como modelos de programação estocástica. Eles são mais realísticos que os modelos determinísticos, e tem por objetivo incorporar a incerteza em suas definições. Essa tese aborda os problemas probabilísticos da classe de problemas de multi-estágio com incerteza e com restrições probabilísticas e com restrições probabilísticas conjuntas. Inicialmente, nós propomos um modelo de administração de ativos e passivos multi-estágio estocástico para a indústria de fundos de pensão brasileira. Nosso modelo é formalizado em conformidade com a leis e políticas brasileiras. A seguir, dada a relevância dos dados de entrada para esses modelos de otimização, tornamos nossa atenção às diferentes técnicas de amostragem. Elas compõem o processo de discretização desses modelos estocásticos Nós verificamos como as diferentes metodologias de amostragem impactam a solução final e a alocação do portfólio, destacando boas opções para modelos de administração de ativos e passivos. Finalmente, nós propomos um “framework” para a geração de árvores de cenário e otimização de modelos com incerteza multi-estágio. Baseados na tranformação de Knuth, nós geramos a árvore de cenários considerando a representação filho-esqueda, irmão-direita o que torna a simulação mais eficiente em termos de tempo e de número de cenários. Nós também formalizamos uma reformulação do modelo de administração de ativos e passivos baseada na abordagem extensiva implícita para o modelo de otimização. Essa técnica é projetada pela definição de um processo de filtragem com “bundles”; e codifciada com o auxílio de uma linguagem de modelagem algébrica. A eficiência dessa metodologia é testada em um modelo de administração de ativos e passivos com incerteza com restrições probabilísticas conjuntas. Nosso framework torna possível encontrar a solução ótima para árvores com um número razoável de cenários