Centre for Advanced Study

at the Norwegian Academy of Science and Letters

Stochastics in environmental and financial economics (SEFE)

Abstract

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

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