Optimal WACC in tariff regulation under uncertainty

In the regulation of network tariffs, the compensation for the opportunity costs of capital through the Weighted Average Costs of Capital (WACC) plays a crucial role. Determining the appropriate level for the WACC is, though, problematic because of the uncertainty about the future conditions in capital markets. When the WACC is set above the future opportunity costs of capital, consumers will pay too much, while when the WACC is below that level, network operators may be unable to finance investments affecting quality of network services. In this paper, we explicitly take this uncertainty into account when we determine the optimal WACC for the tariff regulation of an electricity network. By trading off consumer surplus and expected disruption costs in the electricity grid, we conclude that from a social-welfare perspective in most cases the optimal WACC in tariff regulation is above the historical mean costs of capital. Only in case of high uncertainty about the true costs of capital while network operators are able to quickly increase investment levels, the optimal WACC is below the historical mean because then it is less likely that the WACC is constantly insufficient to cover actual costs of capital. However, when network operators cannot quickly increase investment levels the optimal WACC is always above the historical mean cost of capital

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically nonconvex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q.In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the `1-norm of q

On Proportionally Fair Solutions for the Divorced-Parents Problem

When Dutch parents divorce, Dutch law dictates that the parental contributions to cover the financial needs ofthe children have to be proportionally fair. This rule is clear when parents only have common children. However,cases can be considerably more complicated, for example when parents have financial responsibilities to childrenfrom previous marriages. We show that, mathematically, this settlement problem can be modelled as a bipartiterationing problem for which a unique global proportionally fair solution exists. Moreover, we develop two efficientalgorithms for obtaining this proportionally fair solution, and we show numerically that both algorithms areconsiderably faster than standard convex optimization techniques. The first algorithm is a novel tailor-madefixed-point iteration algorithm, whereas the second algorithm only iteratively applies simple lawsuits involvinga single child and its parents. The inspiration for this latter algorithm comes from our main convergence proofin which we show that iteratively applying settlements on smaller subnetworks eventually leads to the samesettlement on the network as a whole. This has significant societal importance since in practice lawsuits areoften only held between two or a few parents. Moreover, our iterative algorithm is easy to understand, alsoby parents, legal counselors, and judges, which is crucial for its acceptance in practice. Finally, as the methodprovides a unique solution to any dispute, it removes the legal inequality perceived by parents. Consequently, itmay considerably reduce the workload of courts because parents and lawyers can compute the proportionally fairparental contributions before bringing their case to court