Fred Espen Benth

Stochastics: An International Journal of Probability and Stochastic Processes 97(1) s. 55-80 Doi: https://doi.org/10.1080/17442508.2024.2422122

Electronic Journal of Probability (EJP) 29 s. 1-41 Doi: https://doi.org/10.1214/24-EJP1182

Quarterly Journal of the Royal Meteorological Society 150 s. 2712-2726 Doi: https://doi.org/10.1002/qj.4731

There are sparse opportunities for direct measurement of upper stratospheric winds, yet improving their representation in subseasonal-to-seasonal prediction models can have significant benefits. There is solid evidence from previous research that global atmospheric infrasound waves are sensitive to stratospheric dynamics. However, there is a lack of results providing a direct mapping between infrasound recordings and polar-cap upper stratospheric winds. The global International Monitoring System (IMS), which monitors compliance with the Comprehensive Nuclear-Test-Ban Treaty, includes ground-based stations that can be used to characterize the infrasound soundscape continuously. In this study, multi-station IMS infrasound data were utilized along with a machine-learning supported stochastic model, Delay-SDE-net, to demonstrate how a near-real-time estimate of the polar-cap averaged zonal wind at 1-hPa pressure level can be found from infrasound data. The infrasound was filtered to a temporal low-frequency regime dominated by microbaroms, which are ambient-noise infrasonic waves continuously radiated into the atmosphere from nonlinear interaction between counter-propagating ocean surface waves. Delay-SDE-net was trained on 5 years (2014–2018) of infrasound data from three stations and the ERA5 reanalysis 1-hPa polar-cap averaged zonal wind. Using infrasound in 2019–2020 for validation, we demonstrate a prediction of the polar-cap averaged zonal wind, with an error standard deviation of around 12 m·s compared with ERA5. These findings highlight the potential of using infrasound data for near-real-time measurements of upper stratospheric dynamics. A long-term goal is to improve high-top atmospheric model accuracy, which can have significant implications for weather and climate prediction.

Journal of Computational Biology 31(8) s. 727-741 Doi: https://doi.org/10.1089/cmb.2023.0414

Finance and Stochastics 28 s. 1117-1146 Doi: https://doi.org/10.1007/s00780-024-00542-4

Finance and Stochastics 28(4) s. 1035-1076 Doi: https://doi.org/10.1007/s00780-024-00546-0

The Annals of Applied Probability 34(2) s. 2208-2242 Doi: https://doi.org/10.1214/23-AAP2019

Stochastic Processes and their Applications 162 s. 299-337 Doi: https://doi.org/10.1016/j.spa.2023.05.003

Energy Economics 117 Doi: https://doi.org/10.1016/j.eneco.2022.106421

IMA Journal of Management Mathematics 34(1) s. 187-220 Doi: https://doi.org/10.1093/imaman/dpab032

Springer

Applied Stochastic Models in Business and Industry Doi: https://doi.org/10.1002/asmb.2815

Finance and Stochastics 28 s. 81-121 Doi: https://doi.org/10.1007/s00780-023-00520-2

Energies 16(15) Doi: https://doi.org/10.3390/en16155757

The purpose of this paper is to present and discuss pedagogical frameworks and approaches to developing, delivering, and evaluating a new interdisciplinary course within the domain of energy informatics at both Master’s and PhD levels. This study is needed because many papers on sustainable energy engineering education concentrate on course content but provide very little information on the pedagogical methods employed to deliver that content. The proposed new course is called “smart energy and power systems modelling” and is aimed at discussing how mathematical optimization, in the context of computer science, can contribute to more effectively managing smart energy and power systems. Different pedagogical frameworks are discussed and adapted for the specific domain of energy informatics. An ASSURE model coupled with Bloom’s taxonomy is presented for the design of the course and identification of learning objectives; self-regulated learning strategies are discussed to enhance the learning process; a novel model called GPD (Gaussian Progression of Difficulty) for lecture planning was proposed; a teaching-research nexus is discussed for the course planning and enhancement. Adopting qualitative analyses and an inductive approach, this paper offers a thorough reflection on the strengths and weaknesses of the new course, together with improvement possibilities based on fieldwork and direct experience with the students and colleagues. Opportunities and challenges of interdisciplinary teaching are presented in light of real-world experience, with a particular focus on the interaction between mathematics and computer science to study the specific application of energy and power systems.

Communications in statistics. Case studies, data analysis and applications. 9(3) s. 321-349 Doi: https://doi.org/10.1080/23737484.2023.2217137

Energy Economics 118 Doi: https://doi.org/10.1016/j.eneco.2022.106496

We suggest a new methodology for designing robust energy systems. For this, we investigate so-called near-optimal solutions to energy system optimisation models; solutions whose objective values deviate only marginally from the optimum. Using a refined method for obtaining explicit geometric descriptions of these near-optimal feasible spaces, we find designs that are as robust as possible to perturbations. This contributes to the ongoing debate on how to define and work with robustness in energy systems modelling. We apply our methods in an investigation using multiple decades of weather data. For the first time, we run a capacity expansion model of the European power system (one node per country) with a three-hourly temporal resolution and 41 years of weather data. While an optimisation with 41 weather years is at the limits of computational feasibility, we use the near-optimal feasible spaces of single years to gain an understanding of the design space over the full time period. Specifically, we intersect all near-optimal feasible spaces for the individual years in order to get designs that are likely to be feasible over the entire time period. We find significant potential for investment flexibility, and verify the feasibility of these designs by simulating the resulting dispatch problem with four decades of weather data. They are characterised by a shift towards more onshore wind and solar power, while emitting more than 50% less CO2 than a cost-optimal solution over that period. Our work builds on recent developments in the field, including techniques such as Modelling to Generate Alternatives (MGA) and Modelling All Alternatives (MAA), and provides new insights into the geometry of near-optimal feasible spaces and the importance of multi-decade weather variability for energy systems design. We also provide an effective way of working with a multi-decade time frame in a highly parallelised manner. Our implementation is open-sourced, adaptable and is based on PyPSA-Eur.

Annals of Mathematics and Artificial Intelligence 91 s. 75-103 Doi: https://doi.org/10.1007/s10472-022-09824-z

We propose a neural network architecture in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fréchet space X into a Banach space Y. The approximation results are generalising the well known universal approximation theorem for continuous functions from Rn to R, where approximation is done with (multilayer) neural networks Cybenko (1989) Math. Cont. Signals Syst. 2, 303–314 and Hornik et al. (1989) Neural Netw., 2, 359–366 and Funahashi (1989) Neural Netw., 2, 183–192 and Leshno (1993) Neural Netw., 6, 861–867. Our infinite dimensional networks are constructed using activation functions being nonlinear operators and affine transforms. Several examples are given of such activation functions. We show furthermore that our neural networks on infinite dimensional spaces can be projected down to finite dimensional subspaces with any desirable accuracy, thus obtaining approximating networks that are easy to implement and allow for fast computation and fitting. The resulting neural network architecture is therefore applicable for prediction tasks based on functional data.

Stochastic Processes and their Applications 145 s. 241-268 Doi: https://doi.org/10.1016/j.spa.2021.12.011

Stochastics: An International Journal of Probability and Stochastic Processes s. 1-23 Doi: https://doi.org/10.1080/17442508.2021.2019738

Energy Economics 114 Doi: https://doi.org/10.1016/j.eneco.2022.106300

Infinite Dimensional Analysis Quantum Probability and Related Topics 25(2) s. 1-35 Doi: https://doi.org/10.1142/S0219025722500072

We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the Gelfand integral commutes with linear operators. The Skorohod integral is conveniently expressed in terms of a Gelfand integral on Hida distribution space, which forms our prime motivation and example. We extend several results of Skorohod integrals to a general class of pathwise Gelfand integrals. For example, we provide generalizations of the Hida–Malliavin derivative and extend the integration-by-parts formula in Malliavin Calculus. A Fubini-result is also shown, based on the commutative property of Gelfand integrals with linear operators. Finally, our studies give the motivation for two existing definitions of stochastic Volterra integration in Hida space.

Dependence Modeling 10(1) s. 22-28 Doi: https://doi.org/10.1515/demo-2022-0103

Scandinavian Journal of Statistics Doi: https://doi.org/10.1111/sjos.12559

SIAM Journal on Financial Mathematics 12(4) s. 1374-1415 Doi: https://doi.org/10.1137/21M141556X

Modern Stochastics: Theory and Applications (MSTA) 8(3) s. 349-371 Doi: https://doi.org/10.15559/21-VMSTA178

Digital Finance 3 s. 209-248 Doi: https://doi.org/10.1007/s42521-021-00030-w

Infinite Dimensional Analysis Quantum Probability and Related Topics 24(2) Doi: https://doi.org/10.1142/S0219025721500144

International Journal of Theoretical and Applied Finance 24(6 & 7) Doi: https://doi.org/10.1142/S0219024921500345

Quantitative finance (Print) 21(1) s. 165-183 Doi: https://doi.org/10.1080/14697688.2020.1804606

Electronic Journal of Probability (EJP) 26 Doi: https://doi.org/10.1214/21-EJP683

Mathematics 9(2) Doi: https://doi.org/10.3390/math9020124

Stochastics: An International Journal of Probability and Stochastic Processes Doi: https://doi.org/10.1080/17442508.2020.1802458

Journal of Commodity Markets s. 1-13 Doi: https://doi.org/10.1016/j.jcomm.2019.100122

International Journal of Theoretical and Applied Finance 23(4) Doi: https://doi.org/10.1142/S0219024920500272

Quantitative finance (Print) 20(9) s. 1441-1456 Doi: https://doi.org/10.1080/14697688.2020.1733059

IEEE Transactions on Power Systems 35(2) s. 1085-1098 Doi: https://doi.org/10.1109/TPWRS.2019.2938423

Risks 8(1) Doi: https://doi.org/10.3390/risks8010008

Mathematics and Financial Economics 13(4) s. 543-577 Doi: https://doi.org/10.1007/s11579-019-00237-x

Journal of Mathematical Analysis and Applications 476(1) s. 196-214 Doi: https://doi.org/10.1016/j.jmaa.2018.12.055

Stochastic Analysis and Applications 36(4) s. 733-750 Doi: https://doi.org/10.1080/07362994.2018.1461566

Applied Mathematical Finance 25(1) s. 36-65 Doi: https://doi.org/10.1080/1350486X.2018.1438904

Stochastic Processes and their Applications 128(2) s. 461-486 Doi: https://doi.org/10.1016/j.spa.2017.05.005

Mathematics and Financial Economics 13(1) s. 87-114 Doi: https://doi.org/10.1007/s11579-018-0221-8

Transportation Research Part E: Logistics and Transportation Review 113 s. 194-221 Doi: https://doi.org/10.1016/j.tre.2017.10.014

In this paper, we propose a new multivariate model for the dynamics of regional ocean freight rates. We show that a cointegrated system of regional spot freight rates can be decomposed into a common non-stationary market factor and stationary regional deviations. The resulting integrated CAR process is new to the literature. By interpreting the common market factor as the global arithmetic average of the regional rates, both the market factor and the regional deviations are observable which simplifies the calibration of the model. Moreover, forward contracts on the market factor can be traded in the Forward Freight Agreement (FFA) market. We calibrate the model to historical spot rate processes and illustrate the term structures of volatility and correlation between the regional prices and the market factor. Our model is an important contribution towards improved modelling and hedging of regional price risk when derivative market liquidity is concentrated in a single global benchmark.

Finance and Stochastics 22(2) s. 327-366 Doi: https://doi.org/10.1007/s00780-018-0355-9

Risks 6(2) Doi: https://doi.org/10.3390/risks6020056

Computation and Combinatorics in Dynamics, Stochastics and Control s. 297-320 Doi: https://doi.org/10.1007/978-3-030-01593-0_11

Springer Nature

Journal of Energy Markets 10(1) s. 1-25 Doi: https://doi.org/10.21314/jem.2017.157

Stochastics: An International Journal of Probability and Stochastic Processes 89(1) s. 311-347 Doi: https://doi.org/10.1080/17442508.2016.1177057

Real Options in Energy and Commodity Markets s. 63-115 Doi: https://doi.org/10.1142/9789813149410_0003

We conduct an empirical investigation of the logreturns of the futures prices of the European Union Emission Trading System emission certificates traded in the Nord Pool market between 2005 and 2013. We observe heaviness, skewness, and high kurtosis of these logreturns. We thus propose modeling the futures logprices using the Barndorff-Nielsen and Shephard (BNS) or the Heston stochastic volatility models.We carry out an empirical comparison between the performances of these models and investigate their stationary autocorrelation structure. In particular, as a consequence of allowing for skewness in the Heston model, we find analytical expressions for the autocorrelation function of the logreturns and their squares. Our analysis indicates the presence of short-range dependence in the observed futures logprice returns. We conclude that the BNS model better describes the empirical features of the observed futures prices than the Heston model. Our findings have relevance for the real option modeling of fossil-fueled power plants when considering emission costs.

Energy Economics 68 s. 283-302 Doi: https://doi.org/10.1016/j.eneco.2017.10.008

Journal of Energy Markets 10(2) s. 1-39 Doi: https://doi.org/10.21314/JEM.2017.159

We propose and investigate a valuation model for the income of selling tradeable green certificates (TGCs) in the Swedish–Norwegian market, formulated as a singular stochastic control problem. Our model takes into account the production rate of renewable energy from a “typical” plant, the price of TGCs and the cumulative amount of certificates sold.We assume that the production rate has a dynamics given by an exponential Ornstein–Uhlenbeck process, and the logarithmic TGC price has a dynamics given by a Lévy process. For this class of dynamics, we find optimal decision rules for the state variables and a closed-form solution to the control problem. A case study of ICAP prices and wind production data from Denmark backs up our model choice and shows the relevance of this pricing approach.

Journal of Energy Markets 10(3) s. 1-33 Doi: https://doi.org/10.21314/JEM.2017.164

Journal of Banking & Finance 95 s. 203-216 Doi: https://doi.org/10.1016/j.jbankfin.2017.03.018

Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a spatio-temporal dynamical model based on the Heath-Jarrow-Morton (HJM) approach under the Musiela parametrization, which ensures an arbitrage-free model for electricity forward prices. The model is fitted to a unique data set of historical price forward curves. As a particular feature of the model, we disentangle the temporal from spatial (maturity) effects on the dynamics of forward prices, and shed light on the statistical properties of risk premia, of the noise volatility term structure and of the spatio-temporal noise correlation structures. We find that the short-term risk premia oscillates around zero, but becomes negative in the long run. We identify the Samuelson effect in the volatility term structure and volatility bumps, explained by market fundamentals. Furthermore we find evidence for coloured noise and correlated residuals, which we model by a Hilbert space-valued normal inverse Gaussian Lévy process with a suitable covariance functional. (Best Energy Paper Award, ECOMFIN 2016, Paris)

Advanced Modelling in Mathematical Finance s. 477-496 Doi: https://doi.org/10.1007/978-3-319-45875-5_20

The Fascination of Probability, Statistics and their Applications. In honour of Ole E. Barndorff-Nielsen s. 153-189 Doi: https://doi.org/10.1007/978-3-319-25826-3_8

Springer Science+Business Media B.V.

International Journal of Theoretical and Applied Finance 19(1) Doi: https://doi.org/10.1142/S0219024916500023

Bernoulli 22(3) s. 1383-1430 Doi: https://doi.org/10.3150/15-BEJ696

Maritime Economics & Logistics 18(4) s. 391-413 Doi: https://doi.org/10.1057/mel.2015.22

Bernoulli 22(2) s. 774-793 Doi: https://doi.org/10.3150/14-BEJ675

International Journal of Theoretical and Applied Finance 18(6) Doi: https://doi.org/10.1142/S0219024915500387

International Journal of Theoretical and Applied Finance 18(2) Doi: https://doi.org/10.1142/S0219024915500107

Finance and Stochastics 19(4) s. 849-889 Doi: https://doi.org/10.1007/s00780-015-0270-2

Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management s. 801-825 Doi: https://doi.org/10.1002/9781119011590.ch17

IMA Journal of Management Mathematics 26(3) s. 273-297 Doi: https://doi.org/10.1093/imaman/dpu001

SIAM Journal on Financial Mathematics 6(1) s. 825-869 Doi: https://doi.org/10.1137/15100268X

Journal of Energy Markets 18(4) s. 69-92 Doi: https://doi.org/10.21314/jem.2015.133

Stochastics: An International Journal of Probability and Stochastic Processes 87(3) s. 458-476 Doi: https://doi.org/10.1080/17442508.2014.966826

Energy Economics 52 s. 104-117 Doi: https://doi.org/10.1016/j.eneco.2015.09.009

Fields Institute Communications 74 s. 109-148 Doi: https://doi.org/10.1007/978-1-4939-2733-3_5

Journal of Energy Markets 8(1) s. 1-35 Doi: https://doi.org/10.21314/jem.2015.130

Applied Mathematical Finance 22(1) s. 28-62 Doi: https://doi.org/10.1080/1350486X.2014.948708

SIAM Journal on Financial Mathematics 5 s. 685-728 Doi: https://doi.org/10.1137/13093604X

Infinite Dimensional Analysis Quantum Probability and Related Topics 17(2) Doi: https://doi.org/10.1142/S0219025714500118

Stochastics: An International Journal of Probability and Stochastic Processes 86(6) s. 932-966 Doi: https://doi.org/10.1080/17442508.2014.895359

Stochastic Processes and their Applications 124(1) s. 812-847 Doi: https://doi.org/10.1016/j.spa.2013.09.007

Communications in Mathematics and Statistics 2(1) s. 47-106 Doi: https://doi.org/10.1007/s40304-014-0030-1

SIAM Journal on Financial Mathematics 5(1) s. 71-98 Doi: https://doi.org/10.1137/130905320

Energy Pricing Models : Recent Advances, Methods, and Tools s. 223-268 Doi: https://doi.org/10.1007/978-1-137-37027-3_8

Springer Science+Business Media B.V.

Quantitative Energy Finance: Modeling, pricing and hedging in energy and commodity markets s. 285-305 Doi: https://doi.org/10.1007/978-1-4614-7248-3_11

Lecture notes in Energy 54 s. 233-260 Doi: https://doi.org/10.1007/978-3-642-55382-0_10

Finance and Stochastics 18(2) s. 407-430 Doi: https://doi.org/10.1007/s00780-013-0224-5

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.

Energy Economics 44 s. 392-406 Doi: https://doi.org/10.1016/j.eneco.2014.03.020

Journal of Energy Markets 7(2) s. 35-69 Doi: https://doi.org/10.21314/jem.2014.114

International Journal of Theoretical and Applied Finance 17(2) Doi: https://doi.org/10.1142/S0219024914500083

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Recent advances in financial engineering - Proceedings of the International Workshop on Fininance 2012 s. 1-24 Doi: https://doi.org/10.1142/9789814571647_0001

The Interrelationship Between Financial and Energy Markets s. 233-260 Doi: https://doi.org/10.1007/978-3-642-55382-0

Advances in Applied Probability 46(3) s. 719-745 Doi: https://doi.org/10.1239/aap/1409319557

Seminar on Stochastic Analysis, Random Fields and Applications VII - Centro Stefano Franscini, Ascona, May 2011 s. 261-284 Doi: https://doi.org/10.1007/978-3-0348-0545-2_14

Mathematical Modeling with Multidisciplinary Applications s. 257-284 Doi: https://doi.org/10.1002/9781118462706.ch11

SIAM Journal on Scientific Computing 35(5) s. A2207-A2224 Doi: https://doi.org/10.1137/110851080

Advances in Applied Probability 45(2) s. 572-594 Doi: https://doi.org/10.1239/aap/1370870130

Energy Economics 36 s. 55-77 Doi: https://doi.org/10.1016/j.eneco.2012.12.001

Advances in Applied Probability 45(2) s. 545-571 Doi: https://doi.org/10.1239/aap/1370870129

Stochastics: An International Journal of Probability and Stochastic Processes 85(5) s. 833-858 Doi: https://doi.org/10.1080/17442508.2012.665056

Stochastics: An International Journal of Probability and Stochastic Processes 85(6) s. 1015-1039 Doi: https://doi.org/10.1080/17442508.2012.736994

World Scientific

Lecture notes in mathematics 2081 s. 109-167 Doi: https://doi.org/10.1007/978-3-319-00413-6_2

Energy Economics 40 s. 259-268 Doi: https://doi.org/10.1016/j.eneco.2013.07.007

Bernoulli 19(3) s. 803-845 Doi: https://doi.org/10.3150/12-BEJ476

Operations Research 60(6) s. 1373-1388 Doi: https://doi.org/10.1287/opre.1120.1112

Review of Development Finance 2(1) s. 22-31 Doi: https://doi.org/10.1016/j.rdf.2012.01.004

SIAM Journal on Financial Mathematics 3 s. 639-666 Doi: https://doi.org/10.1137/100818261

Energy Economics 34 s. 1589-1616 Doi: https://doi.org/10.1016/j.eneco.2011.11.012

Energy Economics 34(2) s. 592-602 Doi: https://doi.org/10.1016/j.eneco.2011.09.012

Stochastic Analysis and Applications 30(1) s. 20-43 Doi: https://doi.org/10.1080/07362994.2012.628906

Journal of Energy Markets 4(4) s. 3-28 Doi: https://doi.org/10.21314/jem.2011.065

Journal of Energy Markets 5(4) s. 3-31 Doi: https://doi.org/10.21314/jem.2012.080

Journal of Forecasting 30(3) s. 355-376 Doi: https://doi.org/10.1002/for.1179

International Journal of Stochastic Analysis Doi: https://doi.org/10.1155/2011/576791

We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.

Quantitative finance (Print) 11(3) s. 407-421 Doi: https://doi.org/10.1080/14697688.2010.481629

Statistical Tools for Finance and Insurance s. 163-199 Doi: https://doi.org/10.1007/978-3-642-18062-0_5

Statistical research report (Universitetet i Oslo. Matematisk institut

Communications on Stochastic Analysis 5(2) s. 285-307 Doi: https://doi.org/10.31390/cosa.5.2.03

Applied Mathematical Finance 18(2) s. 93-117 Doi: https://doi.org/10.1080/13504861003722385

Advanced Mathematical Methods for Finance s. 35-74 Doi: https://doi.org/10.2139/ssrn.1597697

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis.

Mathematical Finance 21(4) s. 595-625 Doi: https://doi.org/10.1111/j.1467-9965.2010.00445.x

We consider the non-Gaussian stochastic volatility model of Barndorff-Nielsen and Shephard for the exponential mean-reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log-spot prices possess a stationary distribution defined as a normal variance-mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean-reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff-Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.

QUANTUM PROBABILITY AND INFINITE DIMENSIONAL ANALYSIS - Proceedings of the 29th Conference s. 153-184

International Journal of Applied Mathematics and Statistics 16(M10) s. 11-37

Stochastics: An International Journal of Probability and Stochastic Processes 82(3) s. 291-313 Doi: https://doi.org/10.1080/17442501003629554

Journal of Applied Statistics 37(6) s. 893-909 Doi: https://doi.org/10.1080/02664760902914490

Preprint series (Universitetet i Oslo. Matematisk institutt)

AIP Conference Proceedings 1281 s. 531-534 Doi: https://doi.org/10.1063/1.3498530

Alternative Investments and Strategies s. 93-122

Energy Economics 32(5) s. 1034-1043 Doi: https://doi.org/10.1016/j.eneco.2010.01.005

Energy Journal 31(2) s. 53-86

We analyze the daily returns of Nordic electricity swaps and identify significant risk premia in the short end of the market. On average, long positions in this part of the swap market yield negative returns. The daily returns are distinctively non-normal in terms of tail-fatness, but we find little evidence of asymmetry. We investigate if the flexible four-parameter class of normal inverse Gaussian (NIG) distributions can capture the observed stylized facts and find that this class of distributions offers a remarkably improved fit relative to the normal distribution. We also compare the fit with that of the four-parameter class of stable distributions; the NIG law outperforms the stable law in the vast majority of cases. Thus, the NIG family of distributions, which allows for stochastic dynamics in terms of Levy processes that are suitable for pricing derivatives and Value-at-Risk measurements, is a serious candidate for modeling term structure dynamics in the Nordic electricity market.

International Journal of Theoretical and Applied Finance 12(1) s. 63-82 Doi: https://doi.org/10.1142/S0219024909005117

Journal of Energy Markets 2(3) s. 111-140

Energy Economics 31(1) s. 16-24

Daily average wind speeds are dynamically modelled by a continuous-time autoregressive model with seasonal mean and volatility. Futures prices based on an index of aggregated wind speeds are derived, and it is shown that the Samuelson effect breaks down. The volatility of these futures will decrease when approaching maturity, an effect which is explained by the memory in higher-order autoregressive models. (C) 2008 Elsevier B.V. All rights reserved.

Stochastic Analysis and Applications 27(5) s. 875-896 Doi: https://doi.org/10.1080/07362990903136413

Preprint series (Universitetet i Oslo. Matematisk institutt)

International Journal of Theoretical and Applied Finance 12(4) s. 491-506

Energy Economics 31(1) s. 16-24 Doi: https://doi.org/10.1016/j.eneco.2008.09.009

Preprint series (Universitetet i Oslo. Matematisk institutt)

The main objective of this work is to construct optimal temperature futures from available market-traded contracts to hedge spatial risk. Temperature dynamics are modelled by a stochastic differential equation with spatial dependence. Optimal positions in market-traded futures minimizing the variance are calculated. Examples with numerical simulations based on a fast algorithm for the generation of random fields are presented.

Journal of Banking & Finance 32(10) s. 2006-2021 Doi: https://doi.org/10.1016/j.jbankfin.2007.12.022

International Journal of Theoretical and Applied Finance

Journal of Banking & Finance Journal of Banking &(Volum 32 (10)) s. 2006-2021

World Scientific

Energy Economics 30(3) s. 1116-1157 Doi: https://doi.org/10.1016/j.eneco.2007.06.005

World Scientific

Energy Economics 30(3) s. 1116-1157

We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (c) 2007 Elsevier B.V. All rights reserved.

Applied Mathematical Finance 14(2) s. 153-169 Doi: https://doi.org/10.1080/13504860600725031

Journal of Derivatives 15(1) s. 52-66

Journal of Applied Statistics 34(7) s. 823-841 Doi: https://doi.org/10.1080/02664760701511398

Applied Mathematical Finance 14(2) s. 153-169

Quantitative finance (Print) 7(5) s. 553-561 Doi: https://doi.org/10.1080/14697680601155334

Applied Mathematical Finance 14(4) s. 347-363 Doi: https://doi.org/10.1080/13504860601170609

Springer

Scandinavian Journal of Statistics 34 s. 746-767 Doi: https://doi.org/10.1111/j.1467-9469.2007.00564.x

Quantitative finance (Print) 7(5) s. 553-561

We propose an Ornstein-Uhlenbeck process with seasonal volatility to model the time dynamics of daily average temperatures. The model is fitted to approximately 45 years of daily observations recorded in Stockholm, one of the European cities for which there is a trade in weather futures and options on the Chicago Mercantile Exchange. Explicit pricing dynamics for futures contracts written on the number of heating/cooling degree-days (so-called HDD/CDD futures) and the cumulative average daily temperature (so-called CAT futures) are calculated, along with a discussion on how to evaluate call and put options with these futures as underlying.

Scandinavian Journal of Statistics 34(4) s. 746-767

Journal of Derivatives 15(1) s. 52-66

Applied Mathematical Finance 14(4) s. 347-363

International Journal of Theoretical and Applied Finance 9(6) s. 843-867

Studies in Nonlinear Dynamics & Econometrics 10(3)

Stochastics and Stochastics Reports 77(2) s. 109-137

Stochastic Analysis and Applications 23

Finance and Stochastics 9(4) s. 563-575 Doi: https://doi.org/10.1007/s00780-005-0161-z

Applied Mathematical Finance 12(1) s. 53-85

Interfaces and free boundaries (Print) 6 s. 379-404

Applied Mathematics and Optimization 49 s. 27-41

International Journal of Theoretical and Applied Finance 7(2) s. 177-192

Stochastics and Stochastics Reports 76(3) s. 191-211

Mathematical Finance 13(2) s. 215-244

International Journal of Theoretical and Applied Finance 6(8) s. 865-884

International Journal of Theoretical and Applied Finance 6(8) s. 865-884

Applied Mathematical Finance 10(4) s. 303-324

Applied Mathematical Finance 10(4) s. 325-336 Doi: https://doi.org/10.1080/1350486032000160777

Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non‐tradeable. The method is based on the so‐called ‘fitting of the yield curve’ technique from interest rate theory. The spot price dynamics of Schwartz is generalized to multidimensional correlated stochastic processes with Wiener and Lévy noise. Findings are illustrated with examples from oil and electricity markets.

Finance and Stochastics 7(3) s. 277-298

Stochastic Analysis and Applications 20(6) s. 1191-1223

Finance and Stochastics 7(3) s. 277-298

Mathematical Finance 13(2) s. 215-244

Mathematical Finance 13(1) s. 55-72 Doi: https://doi.org/10.1111/1467-9965.t01-1-00005

In a market driven by a Lévy martingale, we consider a claim ;. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for ;: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives, and the corresponding versions of the Clark-Haussmann-Ocone theorem.

Stochastics and Stochastics Reports 74 s. 517-569

Journal of the London Mathematical Society 66(2) s. 1-13

Stochastics and Stochastics Reports 74(3-4) s. 517-569

International Journal of Theoretical and Applied Finance 4(5) s. 711-732

Finance and Stochastics 5(4) s. 447-467

Finance and Stochastics 5(3) s. 275-303

Stochastic Analysis and Applications 19(3) s. 329-341

International Journal of Theoretical and Applied Finance 4(5) s. 711-731

Mathematical Geology 33(6) s. 719-744 Doi: https://doi.org/10.1023/1011078716252

Advances in Applied Probability 32 s. 779-799

Potential Analysis 12(4) s. 385-401

Potential Analysis 12(4) s. 385-401

Statistics and Probability Letters 49 s. 345-354 Doi: https://doi.org/10.1016/S0167-7152(00)00067-5

The Metropolis Adjusted Langevin Algorithm (MALA) samples from complex multivariate densities π. The proposal density is based on a discretized version of a Langevin diffusion, and is well defined only for continuously differentiable densities π. We propose a modified MALA algorithm when this condition is not fulfilled or when π has very rapid variations. The algorithm is illustrated on the Strauss model, for which two different classes of smoothing are proposed. In these examples smoothing gives advantages in terms of reduced asymptotic variance.

Infinite Dimensional Analysis Quantum Probability and Related Topics 2(3) s. 381-396

Ukjent s. 333-338

Letters in Mathematical Physics 43 s. 267-278

Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications 51 s. 215-242

Stochastics and Stochastics Reports 63 s. 313-326

Potential Analysis 8 s. 179-193

Potential Analysis 6 s. 127-148

Journal of Functional Analysis 146(2) s. 382-415

Stochastics and Stochastics Reports 58 s. 349-367

Ukjent

Ukjent

Stochastics and Stochastics Reports 1994(51)

Stochastics and Stochastics Reports 51 s. 293-299

Stochastics and Stochastics Reports 51 s. 195-216

Ukjent 8