A multi-period stochastic portfolio optimization model applied for an airline company in the EU ETS

This paper aims to set up and solve a multi-period stochastic portfolio optimization model from an airline company’s point of view, considering all the specific European Union Emissions Trading Scheme (EU ETS) regulatory, managerial and trading constraints (i.e. physical constraints). Our contribution to existing academic literature is multiple. As the first ever case, we apply this technique to the aviation sector, a newly included sector within the EU ETS. More than mainly incorporating physical and technical (‘engineering’) features and focusing on short-term planning issues, we particularly address financial features and focus on mid-term planning issues. Therefore, instead of using spot prices, we run Monte Carlo simulations of correlated geometric Brownian motions (GBM) for traded futures prices of various emission allowance types for different CO₂ delivery time periods. We thereby specifically refer to the existing exchange-traded emission allowance types EU Emission Allowance (EUA) and Certified Emission Reduction (CER). By implementing actually valid and real-world-oriented regulatory constraints for EU ETS, namely managerial and trading constraints, our model implies a real-life application. We also highlight the possibility of banking and borrowing of emission allowances between CO₂ compliance periods, which is a crucial regulatory feature of EU ETS.     

Price dynamics in the European Union Emissions Trading System and evaluation of its ability to boost emission-related investment decisions

The price of permits in the European Union Emissions Trading System (EU ETS) has historically been highly sensitive and prone to jumps. We consider different stochastic processes to model the price of permits, and show that the Variance Gamma (VG) model provides the best fit for the price distribution, among a selection of infinite activity processes. Using this result as a starting point, we assess the effects of the EU ETS in delivering low-carbon investments at the firm level, by modeling a price taker electricity producer subject to the EU ETS jurisdiction. We compute, via Least Squares Monte Carlo, the value of the real option the greenhouse gas emitter has, consisting in the opportunity to switch from its current high-carbon technology to a cleaner one. We use a VG specification for carbon prices, and a mean-reverting (Brennan–Schwartz) process for the price of fuel. Moreover, we further analyze the investment decision problem, in case of a CO₂ price stabilization mechanism in the form of a price floor, by explicitly computing the expected value of the investment project by means of Fourier methods. Our results show that the introduction of the price stabilization mechanism significantly affects the timing of the investment decision, and supports emission-related investments.     

Supporting hydrogen based transportation: case studies with Global MARKAL Model

Steadily growing prices of oil and emissions coming from conventional vehicles, might force a switch to an alternative and less polluting fuel in the coming future. In this article we analyze the potential influence of selected factors for successful market penetration of hydrogen fuel cell vehicles in hydrogen based private transportation economy. Using a world scale, full energy system, bottom-up, optimization model (Global MARKAL Model—GMM) we address the possibility of supporting the fuel cell vehicle technology to become competitive in the markets. In a series of optimizations we evaluate the potential influence of governmental supports and the internalization of externalities related to CO₂ and local pollution emissions originating from the transportation sector, as well as preferential crediting options and demonstration projects promoting fuel cell vehicles. The results suggest that the crucial element is the price of fuel cells and their further potential to reduce costs. This reduction of costs may be triggered by governmental support such as direct subsidies to fuel cells, preferential crediting options for the buildup of hydrogen infrastructure as well as penalization of emitters of CO₂ and/or local pollutants.     

A stochastic model for investments in different technologies for electricity production in the long period

We present a single stage stochastic mixed integer linear model for determining the optimal mix of different technologies for electricity generation, ranging from coal, nuclear and combined cycle gas turbine to hydroelectric, wind and photovoltaic, taking into account the existing plants, the cost of investment in new plants, maintenance costs, purchase and sale of ${CO}_2$ emission trading certificates and green certificates, in order to satisfy regulatory requirements. The power producer is assumed to be a price-taker. Stochasticity of future fuel prices, which affect the generation variable costs, is included in the model by means of a set of scenarios. The main contribution of the paper, beyond considering stochasticity in the future fuel prices, is the introduction of CVaR risk measure in the objective function in order to limit the possibility of low profits in bad scenarios with a fixed confidence level.     

An efficient linear model and optimisation algorithm for multi-site combined heat and power production

Combined heat and power (CHP) production is an important energy production technology which can help to improve the efficiency of energy production and to reduce the emission of CO₂. Cost-efficient operation of a CHP system can be planned using an optimisation model based on hourly load forecasts. A long-term planning model decomposes into hourly models, which can be formulated as linear programming (LP) problems. Such problems can be solved efficiently using the specialized Power Simplex algorithm. However, Power Simplex can only manage one heat and one power balance. Since heat cannot be transported over long distances, Power Simplex applies only for local CHP planning.In this paper we formulate the hourly multi-site CHP planning problem with multiple heat balances as an LP model with a special structure. We then develop the Extended Power Simplex (EPS) algorithm for solving such models efficiently. Even though the problem can be quite large as the number of demand sites increases, EPS demonstrates very good efficiency. In test runs with realistic models, EPS is from 29 to 85 times faster than an efficient sparse Simplex code using the product form of inverse (PFI). Furthermore, the relative efficiency of EPS improves as the problem size grows.     

Energy and CO2 emission performance in electricity generation: A non-radial directional distance function approach

This paper presents a non-radial directional distance function approach to modeling energy and CO₂emission performance in electricity generation from the production efficiency point of view. We first define and construct the environmental production technologies for the countries with and without CHP plants, respectively. The non-radial direction distance function approach is then proposed and several indexes are developed to measure energy and CO₂ emission performance of electricity generation. The directional distance functions established can be computed by solving a series of data envelopment analysis models. We then conduct an empirical study using the dataset for over one hundred countries. It is found that OECD countries have better carbon emission performance and integrated energy-carbon performance than non-OECD countries in electricity generation, while the difference in energy performance is not significant.     

Local air pollutant emission reduction and ancillary carbon benefits of SO2 control policies: Application of AIM/CGE model to China

While a great deal of literature has been published in recent years on the ancillary benefits of greenhouse gas mitigation (e.g., reductions in local air pollution), less attention has been focused on the climate benefits of local air pollution strategies themselves. Local air pollution is, however, a more immediate issue now faced by developing countries. This study assesses the impacts on local air pollutant emission reduction and ancillary CO₂ emission reduction of SO₂ control policies in China, such as a sulphur tax, SO₂ total emissions control (TEC), and improvement of energy efficiency, based on the Asia-Pacific Integrated Model (AIM)/Computable General Equilibrium (CGE) country model. The simulation period is from 1997 to 2020. Major conclusions include the following: an SO₂ emission cap will help to control SO₂ emissions, but will result in a large GDP loss; the role of a SO₂ emission tax at the present level is very limited; and an ancillary carbon reduction benefit can be achieved through the introduction of SO₂ control policies in China.     

An efficient envelope-based Branch and Bound algorithm for non-convex combined heat and power production planning

Combined heat and power (CHP) production is universally accepted as one of the most energy-efficient technologies to produce energy with lower fuel consumption and fewer emissions. In CHP technology, heat and power generation follow a joint characteristic. Traditional CHP production is usually applied in backpressure plants, where the joint characteristic can often be represented by a convex model. Advanced CHP production technologies such as backpressure plants with condensing and auxiliary cooling options, gas turbines, and combined gas and steam cycles may require non-convex models. Cost-efficient operation of a CHP system can be planned using an optimization model based on forecasts for heat load and power price. A long-term planning model decomposes into thousands of single-period models, which can be formulated in the convex case as linear programming (LP) problems, and in the non-convex case as mixed integer programming (MIP) problems.     

Two-agent Pareto optimal cooperative investment in general semimartingale model

We consider the problem of expected utility maximization for the two-agent case in general semimartingale model. For this case a cooperative investment game is posed as follows: firstly collect both agents' capital as a whole at the initial time, and invest it in a trading strategy. Then at some time T ₀ one agent quits cooperation and terminates investment, so they divide the wealth and each of them gets a part. During the time interval [T ₀, T], the other agent invests her capital in a new trading strategy herself. By stochastic optimization methods with the help of the theory of backward stochastic differential equations, we give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non-cooperation in our model.     

Does EU ETS instigate Air Cargo network reconfiguration? A model-based analysis

From 2012 on aviation is included in the European Emissions Trading Scheme (EU ETS) and operators have to hold one allowance per tonne of CO₂ emitted on every flight departing from and/or arriving at an airport within the EU. Now two questions are of interest: Is it profitable for airlines to reconfigure their routes to reduce EU-related emissions and costs, and, will the scheme be successful in the sense that emissions are reduced significantly. Here the potential for and the consequences of reconfiguration are different for the passenger and cargo business, respectively. In this paper we present a model-based evaluation of network (re-)configuration/optimization at cargo airlines under different EU ETS scenarios and we discuss the results with respect to the two issues raised above.     

A risk management system for sustainable fleet replacement

This article analyzes the fleet management problem faced by a firm when deciding which vehicles to add to its fleet. Such a decision depends not only on the expected mileage and tasks to be assigned to the vehicle but also on the evolution of fuel and CO₂ emission prices and on fuel efficiency. This article contributes to the literature on fleet replacement and sustainable operations by proposing a general decision support system for the fleet replacement problem using stochastic programming and conditional value at risk (CVaR) to account for uncertainty in the decision process. The article analyzes how the CVaR associated with different types of vehicle is affected by the parameters in the model by reporting on the results of a real-world case study.     

On the Modeling of CO2 EUA and CER Prices of EU‐ETS for the 2008–2012 Period

Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008–2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average–generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008–2012. Data‐driven methods for identifying possible change‐points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change‐points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change‐points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change‐points seem to parallel the global economic indicators as well. Copyright © 2016 John Wiley & Sons, Ltd.     

An Activity-Based Costing decision model for life cycle assessment in green building projects

Carbon emissions are an increasingly important consideration in sustainable environmental development. In the green building industry, green construction cost controls and low-carbon construction methods are considered to be the key barriers encountered. Based on Corporate Social Responsibility (CSR) policy, management of carbon emissions from green building projects contributes to the acquisition of accurate building cost information and to a reduction in the environmental impact of these projects. This study focuses on the CO₂ emission costs and low-carbon construction methods, and proposes a 0–1 mixed integer programming (0–1 MIP) decision model for integrated green building projects, using an Activity-Based Cost (ABC) and life cycle assessment (LCA) approach. The major contributions of this study are as follows: (1) the integrated model can help construction company managers to more accurately understand how to allocate resources and funding for energy saving activities to each green building through appropriate cost drivers; (2) this model provides a pre-construction decision-making tool which will assist management in bidding on environmentally-friendly construction projects; and (3) this study contributes to the innovation operation research (OR) literature, especially in regard to incorporating the life cycle assessment measurement into construction cost management by utilizing a mixed decision model for green building projects.     

Modelling a sector undergoing structural change: The case of Danish energy supply

This paper examines structural change in the power and heat producing sector (energy supply) and its implications for the economy. An integrated approach is used to describe the interactions between this sector and the rest of the economy. Thus, a very detailed model of the sector for Denmark has been linked to a macroeconometric model of the Danish economy. It is argued that analysing sectors that undergo radical changes, for example the energy supply sector, should be undertaken by using a model that describes the technological and organisational changes in production along with implications for the demand of the produced goods. Environmental priorities and targets for emission reductions are important for defining energy policy in Denmark. As the energy supply sector at present is a major contributor to emissions of CO₂ and SO₂, knowledge of this sector is vital for reducing these emissions. It is shown that quite substantial emission reductions are possible without encountering a substantial negative impact on the economy. The reduction potential through such economic incentives as fuel taxes is shown to be very sensitive to the technology used at present and in the future. This study also emphasises that the large reduction potential of emissions from the energy supply sector is a one-time gain. Fuel switching and increasing use of wind power cannot be repeated. Scenarios carried out with the combined model show that emission reduction in the energy supply sector will decrease the share of this sector in total emissions remarkably, and that the importance of the sector as a key element in any overall emission reduction strategy will decline. This revised version was published online in June 2006 with corrections to the Cover Date.     

A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times,nonlinear purchase and shortage cost functions

In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. The proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint function, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated into the model. The proposed model is first a nonlinear mixed integer programming which is converted into a linear one by applying some theoretical and numerical techniques. Due to the convexity of the model, the local solution obtained from linear programming solvers is also the global solution. Finally, a numerical example is presented to demonstrate the validity of the proposed model.     

Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer

From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.     

Recursive Algorithms for Trailing Stop: Stochastic Approximation Approach

Trailing stops are often used in stock trading to limit the maximum of a possible loss and to lock in a profit. This work develops stochastic approximation algorithms to estimate the optimal trailing stop percentage. A stochastic optimization approach is proposed to recursively estimate the desired trailing stop percentage. A modification using projection is developed to ensure that the approximation sequence constructed stays in a reasonable range. Convergence of the algorithm is obtained. Moreover, interval estimates are constructed. Simulation examples are presented to compare our algorithm with Monte Carlo methods. Finally, we use real market data to demonstrate the algorithms.     

Financial valuation of investments in future power generation technologies: nuclear fusion and CCS in an emissions trading system

This paper outlines a model approach for the financial valuation of future power generation technologies, such as nuclear fusion or carbon capture and storage (CCS) under an emissions trading regime. Since on imperfect markets, interdependencies between decisions inhibit the isolated valuation of an investment, we use simultaneous calculation of optimal production, sales and investment programs; these are subject to the constraints and conditions characteristic for investments in low- and zero-carbon technologies such as fusion and CCS. Duality theory allows to derive, identify and economically interpret the determinants for the price ceiling as (corrected) net present values. Sensitivity analysis shows how changes in the technical specification or environmental policies affect the maximum payable price. Particularly, tradable permits have several effects on low-carbon investments and do not always encourage CO ₂ abatement. While a zero-emissions technology like fusion always profits from a tightened emissions trading scheme, for low-carbon technology like CCS—in particular cases—this may even be counterproductive from an economic as well as an environmental point of view.     

Development of an energy-emission model using fuzzy sets

In searching for cost-efficient strategies to reduce emissions from energy conversion, most western countries use energy-emission models. In these models, the whole energy conversion chain and possible future options for energy supply and emission reduction are mapped into a network of energy flows. Total discounted cost of energy supply and emission reduction is minimized under the restriction of maximum allowed emissions of SO₂, NO _x , or CO₂. The present paper extends one of these models to allow for fuzzy parameters. Such an extension appears to be useful when the data situation is weak. In this paper, a fuzzy linear program is developed, which has been applied to an energy-emission model of Lithuania.     

The emissions trading paradox

This article considers the price history of CO₂ allowances in the EU Emission Trading Scheme. Since European Emissions Trading started in 2005, the prices of allowances have varied between less than one and thirty Euro per ton of CO₂. This previously unpredicted volatility and, more notably, a significant price crash in May 2005 led to the hypothesis that electricity producers might use their market power to influence the prices of allowances. Besides market power, the combination of information asymmetry and price interdependencies (between prices of primary goods – especially electricity – and allowances) plays an important role in explaining the emissions trading paradox. The model presented will show that banking can lead to such a price crash if market participators act rationally. Furthermore, in such a scenario banking can be profitable for sellers at the cost of buyers.