Essays on risk management in portfolio optimization and gas supply networks

This work focuses on developing algorithms and methodologies to solve problems dealing with uncertainty in portfolio optimization and industrial gas networks. First, we study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio\u27s Net-Present Value (NPV) and the reward is measured by the portfolio\u27s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from thePSPLIB library of project scheduling problems. Both approaches are empirically shown to be effective and outperforming the default benchmark MIQP solver to find near-optimal solutions for the selected instances of the MSVP problem.Second, we present an algorithm to compute near-optimal Value-at-Risk (VaR) portfolios. It is known to be difficult to compute optimal VaR portfolios; that is, an optimal risk-reward portfolio allocation using VaR as the risk measure. This is due to VaR being non-convex and of combinatorial nature. In particular, it is well-known that the VaR portfolio problem can be formulated as a mixed-integer linear program (MILP) that is difficult to solve with current MILP solvers for medium to large-scale instances of the problem. The proposed algorithm addresses the shortcomings of the MILP formulation in terms of solution time. To illustrate the efficiency of the presented algorithm, numerical results are presented using historical asset returns from the US financial market. Empirical results suggest that the developed algorithm obtaining a lower bound for VaR outperforms the recently proposed algorithms from the literature. Additionally, we also show that the developed algorithms are able to obtain and guarantee near-optimal solutions for large scale instances of VaR portfolio optimization problem more efficiently than the off the shelf commercial solvers within 1% accuracy.Third, we analyze the impact of the sensor reading errors on parameters that affect the production costs of a leading US industrial gas supply company. For this purpose, a systematic methodology is applied first to determine the relationship between the system output and input parameters, and second to identify the assigned input sensors whose readings need to be improved in a prioritized manner based on the strength of those input-output relationships. The two main criteria used to prioritize these sensors are the decrease in production costs and the decrease in production costs’ volatility obtained when the selected sensor’s precision is improved. To illustrate the effectiveness of the proposed approach, we first apply it to a simplified version of the real supply network model where the results can be readily validated with the simulated data. Then, we apply and test the proposed approach in the real supply network model with historical data. The experiments suggest that we are able to obtain a significant decrease in production costs and in production costs’ volatility by prioritizing the sensors\u27 maintenance subject to a limited budget.Finally, we analyze the performance of portfolio allocation strategies using clustering techniques based on financial asset\u27s correlation matrices. The Markowitz\u27s mean-variance framework uses first and second order sample moment estimators which are highly subject to estimation errors. The estimation error on the moments could be very significant and it may offset the benefits obtained from the diversification of the portfolio. There are a number of methodologies proposed in the literature to reduce the effect of the estimation error on the moment estimators. A group of these are based on the clustering approaches using sample correlation coefficients as the similarity measure. The idea is to obtain a hierarchical structure between the financial assets and then to use this information to filter the underlying true representative economic information between the assets and to reflect it in a modified correlation matrix. The objective of this study is to replicate and verify some of the published work comparing different allocation strategies and also incorporating recently published hierarchical clustering based portfolio selection strategies into out of sample performance evaluation across different datasets. Initial findings suggest that the difference between the performance of the classical strategies and the recently developed clustering based methodologies are not statistically significant from each other when only positive weights are allowed in the portfolios

Computing near-optimal Value-at-Risk portfolios using integer programming techniques

Value-at-Risk (VaR) is one of the main regulatory tools used for risk management purposes. However, it is difficult to compute optimal VaR portfolios; that is, an optimal risk-reward portfolio allocation using VaR as the risk measure. This is due to VaR being non-convex and of combinatorial nature. In particular, it is well-known that the VaR portfolio problem can be formulated as a mixed-integer linear program (MILP) that is difficult to solve with current MILP solvers for medium to large-scale instances of the problem. Here, we present an algorithm to compute near-optimal VaR portfolios that takes advantage of this MILP formulation and provides a guarantee of the solution’s near-optimality. As a byproduct, we obtain an algorithm to compute tight upper bounds on the VaR portfolio problem that outperform related algorithms proposed in the literature for this purpose. The near-optimality guarantee provided by the proposed algorithm is obtained thanks to the relation between minimum risk portfolios satisfying a reward benchmark and the corresponding maximum reward portfolios satisfying a risk benchmark. These alternate formulations of the portfolio allocation problem have been frequently studied in the case of convex risk measures and concave reward functions. Here, this relationship is considered for general risk measures and reward functions. To illustrate the efficiency of the presented algorithm, numerical results are presented using historical asset returns from the US financial market

Systematic Prioritization of Sensor Improvements in an Industrial Gas Supply Network

The paper analyzes the impact of the sensor reading errors on parameters that affect the production costs of a leading US industrial gas supply company. For this purpose, a systematic methodology is applied first to determine the relationship between the system output and input parameters and second to identify the assigned input sensors whose readings need to be improved in a prioritized manner based on the strength of those input-output relationships. The two main criteria used to prioritize these sensors are the decrease in production costs and the decrease in production costs’ volatility obtained when the selected sensor’s precision is improved. To illustrate the effectiveness of the proposed approach, we first apply it to a simplified version of the real supply network model where the results can be readily validated with the simulated data. Next, we apply and test the proposed approach in the real supply network model with historical data