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 lower 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.
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.
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