arXiv subjects

E. Ruben van Beesten

Publications and source records attributed to E. Ruben van Beesten.

7 recordsLinked to original sources

arXiv2026

Quantifying the degree of risk aversion of spectral risk measures

This paper introduces a quantitative notion of the degree of risk aversion of spectral risk measures. We define a family of degree functionals characterized by three axioms governing normalization, mixtures, and continuity. The resulting degrees admit representations in terms of both the Kusuoka measure and the dual utility function, leading to connections with generalized means, the Gini coefficient, and an Arrow-Pratt-type measure of curvature. We further relate the parameter of the degree functional to the tail behavior of losses through generalized Pareto distributions, which provides an interpretation of the parameter choice and a basis for calibrating spectral risk measures according to their desired treatment of different tail behaviors. The degree functional is consistent with several dominance relations between dual utility functions, and the full degree profile uniquely identifies a spectral risk measure. Finally, we extend the degree functional to law-invariant coherent risk measures through their minimal Kusuoka representations.

q-fin.RM↗

arXiv2025

Assessing solution quality in risk-averse stochastic programs

In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard estimators are optimistically biased, which compromises the statistical guarantee on the optimality gap. We introduce estimators for risk-averse problems that do not suffer from this bias. Our method relies on using two independent samples, each estimating a different component of the optimality gap. Our approach extends a broad class of optimality gap estimation methods from the risk-neutral case to the risk-averse case, such as the multiple replications procedure and its one- and two-sample variants. We show that our approach is tractable and leads to high-quality optimality gap estimates for spectral and quadrangle risk measures. Our approach can further make use of existing bias and variance reduction techniques.

math.OC↗

arXiv2024

STraM: A strategic network design model for national freight transport decarbonization

National freight transport models are valuable tools for assessing the impact of various policies and investments on achieving decarbonization targets under different future scenarios. However, these models struggle to address several critical elements necessary for strategic planning, such as the development and adoption of new fuel technologies over time, inertia in transport fleets, and uncertainty surrounding future transport costs. In this paper, we develop a strategic network design model, named STraM, that explicitly incorporates these key factors. STraM provides a network design plan that includes infrastructure investments and fuel technology decisions, aiming to achieve cost-effective decarbonization of the freight transport system. The model's output can be used as input for higher-resolution national freight transport models to yield results with greater operational detail. We demonstrate the application of STraM through a case study of Norway, offering valuable insights into the strategic planning of sustainable freight transport.

econ.GN↗

arXiv2022

Economic incentives for capacity reductions on interconnectors in the day-ahead market

We consider a zonal international power market and investigate potential economic incentives for short-term reductions of transmission capacities on existing interconnectors by the responsible transmission system operators (TSOs). We show that if a TSO aims to maximize domestic total welfare, it often has an incentive to reduce the capacity on the interconnectors to neighboring countries. In contrast with the (limited) literature on this subject, which focuses on incentives through the avoidance of future balancing costs, we show that incentives can exist even if one ignores balancing and focuses solely on welfare gains in the day-ahead market itself. Our analysis consists of two parts. In the first part, we develop an analytical framework that explains why these incentives exist. In particular, we distinguish two mechanisms: one based on price differences with neighboring countries and one based on the domestic electricity price. In the second part, we perform numerical experiments using a model of the Northern-European power system, focusing on the Danish TSO. In 97% of the historical hours tested, we indeed observe economic incentives for capacity reductions, leading to significant welfare gains for Denmark and welfare losses for the system as a whole. We show that the potential for welfare gains greatly depends on the ability of the TSO to adapt interconnector capacities to short-term market conditions. Finally, we explore the extent to which the recently introduced European "70%-rule" can mitigate the incentives for capacity reductions and their welfare effects.

econ.GN↗

arXiv2022

Pragmatic distributionally robust optimization for simple integer recourse models

Inspired by its success for their continuous counterparts, the standard approach to deal with mixed-integer recourse (MIR) models under distributional uncertainty is to use distributionally robust optimization (DRO). We argue, however, that this modeling choice is not always justified, since DRO techniques are generally computationally extremely challenging when integer decision variables are involved. That is why we propose a fundamentally different approach for MIR models under distributional uncertainty aimed at obtaining models with improved computational tractability. For the special case of simple integer recourse (SIR) models, we show that tractable models can be obtained by pragmatically selecting the uncertainty set. Here, we consider uncertainty sets based on the Wasserstein distance and also on generalized moment conditions. We compare our approach with standard DRO and discuss potential generalizations of our ideas to more general MIR models. An important side-result of our analysis is the derivation of performance guarantees for convex approximations of SIR models. In contrast with the literature, these error bounds are not only valid for continuous distribution, but hold for any distribution.

math.OC↗

arXiv2022

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 in which the second-stage problem has integer decision variables and uncertainty in the second-stage cost vector, technology matrix, and the right-hand side vector. Such mixed-integer recourse models are typically non-convex and thus 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 fact, the only error bound that is known hinges on the assumption that $q$ has a finite support. In this paper, we derive parametric error bounds whose dependence on the distribution of $q$ is explicit and that hold for any distribution of $q$, provided it has a finite expected $\ell_1$-norm. We find that the error bounds scale linearly in the expected value of the $\ell_1$-norm of $q$.

math.OC↗

arXiv2022

Welfare compensation in international transmission expansion planning under uncertainty

In transmission expansion planning, situations can arise in which an expansion plan that is optimal for the system as a whole is detrimental to a specific country in terms of its expected economic welfare. If this country is one of the countries hosting the planned capacity expansion, it has the power to veto the plan and thus, undermine the system-wide social optimum. To solve this issue, welfare compensation mechanisms may be constructed that compensate suffering countries and make them willing to participate in the expansion plan. In the literature, welfare compensation mechanisms have been developed that work in expectation. However, in a stochastic setting, even if the welfare effect after compensation is positive in expectation, countries might still be hesitant to accept the risk that the actual, realized welfare effect may be negative in some scenarios. In this paper we analyze welfare compensation mechanisms in a stochastic setting. We consider two existing mechanisms, lump-sum payments and purchase power agreements, and we develop two novel mechanisms, based on the flow through the new transmission line and its economic value. Using a case study of the Northern European power market, we investigate how well these mechanisms succeed in mitigating risk for the countries involved. Using a theoretically ideal model-based mechanism, we show that there is a significant potential for mitigating risk through welfare compensation mechanisms. Out of the four practical mechanisms we consider, our results indicate that a mechanism based on the economic value of the new transmission line is most promising.

econ.GN↗