Centre for Advanced Study

at the Norwegian Academy of Science and Letters

Stochastics in environmental and financial economics (SEFE)


Norway is a country rich on natural resources. Wind, rain and snow provide us with a huge resource for clean energy production, while oil and gas have since the early 70ties contributed significantly to our economic wealth. Nowadays the income from oil and gas exploitation is invested in the world’s financial markets to ensure the welfare of coming generations. With global concerns about our climate, renewable resources for power generation become more and more important. Bad management of these resources will be a waste that is “cheap” to avoid given the right tools.

The purpose of the SEFE center will be to focus on analysis and management of risk in the environmental and financial economics. We aim at proposing new mathematical models for describing the uncertain dynamics in time and space of weather factors like wind, precipitation and temperature, along with sophisticated models for pricing in energy, commodity and more conventional financial markets. Given such models, which naturally will be formulated in the language of stochastic analysis, our aim is to analyze problems of risk management. These will require new methods for optimal stochastic control theory.

Our program will focus on two major aspects of applications:

The modeling and analysis of environmental economic risk factors. Here we address the core issue of modeling the three major environmental factors: temperature, wind, and rainfalls. We consider the factors separately, but also their interdependencies as well as the interdependencies with the energy prices. To this aim we intend to introduce and study new stochastic models mathematically based on the family of ambit fields. The mathematical questions we intend to address are: the study of dependence via copulas, stochastic integration and differentiation, and integral representations

The management of risk in financial and environmental economics. Here we address problems of hedging and risk minimization. The problem of hedging is tackled by an application of stochastic differentiation and integral representation. To analyze and solve problems of risk minimization we have to address the question of risk measurement. A natural class of risk measures can be obtained by studying associated backward stochastic differential equations. Then the risk minimization problem can be properly addressed. This leads to the study of forward‐backward systems of differential equations and to the study of differential games. Within the management of risk, we intend to address particularly systemic risk as the intrinsic risk of a system where various agents are taking part. This leads to the study of mean‐field stochastic differential equations

End Report

Our experience with research in mathematics is that any new problem that we study, typically leads to several new and challenging problems. This was the case during our year at CAS as well. However, answers to these new problems shed light on the original ones in unexpected ways. For example, we developed some new mathematical models for cross-commodity markets using rather sophisticated random fields. The models came up as generalizations of the ones proposed in the research plan. These models open new questions concerning estimation and simulation, in order to be applicable in concrete market situations. We are following up these aspects in current research collaborations.

Another example comes from the need of pricing contracts in clearly incomplete markets where risks also come from exogenous environmental sources. We have adopted the so-called risk-indifference approach and we have developed techniques of stochastic analysis mixed with convex analysis to analyse the pricing systems. This led to new mathematical results that are now followed up into the application of financial pricing. Indeed this was in the original project description, but the research followed an unexpected line yielding to additional results.

A a new class of stochastic volatility models for commodity and energy futures markets was developed during our year at CAS. These models allow for a more flexible and realistic description of the stochasticity along the various futures contracts on the term structure curve. Our approach calls for new developments in the direction of pricing and hedging derivatives. Mathematical theory for pricing and hedging derivatives on futures contracts in commodity markets was also developed. We also introduced a new cross-commodity model, significantly going beyond the proposed models in the research plan. To fit such random field models to actual markets, we adopted the so-called kriging method to commodity markets. In a rather simplified framework, it shows how the econometric concept of co-integration works in commodity markets. Co-integration is a theoretical framework for linking the stochastic dynamics of two or more assets. We demonstrate how co-integrated commodity spot markets impacts the futures markets, in particular, leading to a specific correlation term structure which has huge consequences on spread option pricing compared with the conventional co-integration theory.

We also took up the investigation of the model and random fields presented in the research project. One of the results obtained at present is an extension of the Malliavin calculus techniques beyond the classical setting of square integrable random variables. This is suitable for the application to models that have so-called large-tails, that is, a comparatively large probability of happening of extreme events.

We have also worked on the management of risk developing a stochastic control for Volterra type equations, which are indeed models of the type presented in the research project. In doing this, we used techniques of Malliavin calculus. The studies will continue, to include application to large systems and network modelled by mean-field.

The financial means and administrative support of CAS made it possible to attract some of the world-leading researchers to Oslo to work with us on mathematical challenges in stochastic analysis, finance, energy and weather. To collaborate with excellent scientists sharpens the mind, as well as bringing up new and original ideas and solutions. A targeted group of international collaborators, working as one group in Oslo, enabled us to make significant breakthroughs on the problems suggested in the research plan. In addition, we have a bundle of new challenges that we will continue studying in our collaborations.


  • Corcuera, José Manuel
    Professor University of Barcelona 2014/2015
  • Coulon, Michael Charles
    Lecturer University of Sussex 2014/2015
  • Khedher, Asma
    Dr. Technical University of Munich 2014/2015
  • Kiesel, Ruediger
    Professor University of Duisburg-Essen 2014/2015
  • Russo, Francesco
    Professor ENSTA ParisTech 2014/2015
  • Rüdiger-Mastandrea, Barbara
    Professor University of Wuppertal 2014/2015
  • Suess, André
    Postdoctoral Fellow Universitat de Barcelona 2014/2015
  • Vanmaele, Michèle
    Professor Ghent University 2014/2015
  • Vives, Josep
    Professor University of Barcelona 2014/2015
  • Øksendal, Bernt Karsten
    Professor University of Oslo (UiO) 2014/2015

Previous events


Group leader

  • Fred Espen Benth

    Title Professor Institution University of Oslo (UiO) Year at CAS 2014/2015
  • Giulia Di Nunno

    Title Professor Institution University of Oslo (UiO) Year at CAS 2014/2015