arXiv subjects

Tommi Ekholm

Publications and source records attributed to Tommi Ekholm.

5 recordsLinked to original sources

arXiv2025

Solving decision problems with endogenous uncertainty and conditional information revelation using influence diagrams

Mathematical programming formulations of influence diagrams can bridge the gap between representing and solving decision problems. However, they suffer from both modeling and computational limitations. Aiming to address modeling limitations, we show how to incorporate conditionally observed information within the mathematical programming representation of the influence diagram. Multi-stage stochastic programming models use conditional non-anticipativity constraints to represent such uncertainties, and we show how such constraints can be incorporated into the influence diagram formulations. This allows us to consider the two main types of endogenous uncertainty simultaneously, namely decision-dependent information structure and decision-dependent probability distribution. Additionally, we apply a subdiagram decomposition to improve both computational efficiency and modeling capabilities. Under suitable conditions, this decomposition allows for considering continuous decision variables arising from, e.g., investment sizing decisions, leading to better solutions than a discretization of the continuous decisions. Finally, our proposed framework is illustrated with a large-scale cost-benefit problem regarding climate change mitigation, simultaneously considering technological research and development, and optimal emission trajectories.

math.OC↗

arXiv2024

A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.

math.OC↗

arXiv2021

Revenue and risk of variable renewable electricity investment: the cannibalization effect under high market penetration

The market revenue for variable renewable electricity (VRE) assets has been under intense scrutiny during the last few years. The observation that wind and solar power depress market prices at times when they produce the most has been termed the 'cannibalization effect'. This can have a substantial impact on the revenue of these technologies, the magnitude of which has already been established within the economic literature on current and future markets. Yet, the effect is neglected in the capital budgeting literature assessing green investments in the electricity sector (e.g. including methods such as portfolio- and real-options theory). In this paper, we present an analytical framework that explicitly models the correlation between VRE production and electricity price, as well as the impact on revenues of the surrounding capacity mix and cost to emit CO$_2$. In particular, we derive closed-form expressions for the short-term and long-term expected revenue, the variance of the revenue and the timing of investments. The effect of including these system characteristics is illustrated with numerical examples, using a wind investment in the Polish electricity system as a test case. We find the cannibalization effect to have major influence on the revenues, making the projected profit of a project decrease from 33% to between 13% and -40% (i.e. a loss), depending on the assumption for the rate of future VRE capacity expansion. Using a real options framework, the investment threshold increases by between 13% and 67%, due to the inclusion of cannibalization. Our results likewise indicate that subjective beliefs and uncertainty about the future electricity capacity mix, e.g.\ VRE capacity growth, significantly affect the assessment of the revenue and investment timing.

physics.soc-ph↗

arXiv2019

Optimal forest rotation under carbon pricing and forest damage risk

Forests will have two notable economic roles in the future: providing renewable raw material and storing carbon to mitigate climate change. The pricing of forest carbon leads to longer rotation times and consequently larger carbon stocks, but also exposes landowners to a greater risk of forest damage. This paper investigates optimal forest rotation under carbon pricing and forest damage risk. I provide the optimality conditions for this problem and illustrate the setting with numerical calculations representing boreal forests under a range of carbon prices and damage probabilities. The relation between damage probability and carbon price towards the optimal rotation length is nearly linear, with carbon pricing having far greater impact. As such, increasing forest carbon stocks by lengthening rotations is an economically attractive method for climate change mitigation, despite the forest damage risk. Carbon pricing also increases land expectation value and reduces the economic risks of the landowner. The production possibility frontier under optimal rotation suggests that significantly larger forests carbon stocks are achievable, but imply lower harvests. However, forests' societally optimal role between these two activities is not yet clear-cut; but rests on the future development of relative prices between timber, carbon and other commodities dependent on land-use.

econ.GN↗

arXiv2015

Optimal forest rotation age under efficient climate change mitigation

This paper considers the optimal rotation of forests when the carbon flows of forest growth and harvest are priced with an increasing price. Such an evolution of carbon price is generally associated with economically efficient climate change mitigation, and would provide incentives for the land-owner for enhanced carbon sequestration. With an infinitely long sequence of even-aged forest rotations, the optimal harvest age changes with subsequent rotations due to the changing carbon price. The first-order optimality conditions therefore also involve an infinite chain of lengths for consecutive forest rotations, and allow the approximation of the infinite-time problem with a truncated series of forest rotations. Illustrative numerical calculations show that when starting from bare land, the initial carbon price and its growth rate both primarily increase the length of the first rotation. With some combinations of the carbon pricing parameters, the optimal harvest age can be several hundred years if the forest carbon is released to the atmosphere upon harvest. This effect is not, however, entirely monotonous. Consequently, the currently optimal harvest ages are generally lower with higher rates of carbon price increase. This creates an interesting temporal aspect, suggesting that the supply of wood and carbon sequestration by forests can change considerably during subsequent rotations under an increasing price on carbon.

econ.GN↗