Pricing ultra-long-dated pension liabilities under the market-consistent valuation is challenged by the scarcity of the long-term market instruments that match or exceed the terms of pension liabilities. We develop a robust self-financing hedging strategy which adopts a min–max expected shortfall hedging criterion to replicate the long-dated liabilities for agents who fear parameter misspecification. We introduce a backward robust least squares Monte Carlo method to solve this dynamic robust optimization problem. We find that both naive and robust optimal portfolios depend on the hedging horizon and the current funding ratio. The robust policy suggests taking more risk when the current funding ratio is low. The yield curve constructed by the robust dynamic hedging portfolio is always lower than the naive one but is higher than the model-based yield curve in a low-rate environment.

We considered a pension fund that needs to hedge uncertain long-term liabilities. We modeled the pension fund as a robust investor facing an incomplete market and fearing model uncertainty for the evolution of its liabilities. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst-case scenario by means of solving a min–max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy.

The present paper addresses the class of two-stage robust optimization problems which canbe formulated as mathematical programs with uncertainty on the right-hand sidecoefficients (RHS uncertainty). The wide variety of applications and the fact that manyproblems in the class have been shown to be NP-hard, motivates the search for efficientlysolvable special cases. Accordingly, the first objective of the paper is to provide anoverview of the most important applications and of various polynomial or pseudo-polynomialspecial cases identified so far. The second objective is to introduce a new subclass ofpolynomially solvable robust optimization problems with RHS uncertainty based on theconcept of state-space representable uncertainty sets. A typicalapplication to a multi period energy production problem under uncertain customer loadrequirements is described into details, and computational results including a comparisonbetween optimal two-stage solutions and exact optimal multistage strategies arediscussed.

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0–1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial problems. This approach is numerically tested on knapsack and multi-dimensional knapsack problems. The results obtained outperform many methods based on earlier literature.

In telecommunications network design, one of the most frequentproblems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, theserequirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technologydevelopment and customer movement due to competitiveness, thedemands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a majorconsideration. In this work, we propose a min-max-min formulation and a methodology to cope with this uncertainty. We model the uncertainty as the convex hull of certain scenarios and show thatcutting plane methods can be applied to solve the underlying problems. We will compare Kelley, Elzinga-Moore and bundle methods.