Preface

On 12th April 2015, Bernt Øksendal turned 70. This is a Special Issue marking his anniversary after the scientific meeting held in Oslo in his honour.

Bernt has a charismatic and inspirational personality, always considerate of all mathematicians, as young or as senior as they might be, scattered all over the world and diverse in gender, beliefs, and traditions. Bernt has been a guide and a mentor for many and certainly for us who write these notes.

A number of world-renowned mathematicians attended the meeting together with a large number of the youngest ones who form the coming generation. Indeed, despite the age differences, many in the audience had made their first steps in stochastic analysis by (virtually) walking through the pages of Bernt’s famous book Stochastic Differential Equation: An Introduction with Applications.

We were delighted by both the number in attendance and the joyful atmosphere. For this we thank all the participants and speakers who so illuminated the occasion. In particular we thank all those that have contributed to this volume, commemorating this event through time.

The Conference in Stochastics for Environmental and Financial Economics (SEFE) was held in Oslo at the Norwegian Royal Academy of Science and Letters, 20–24 April 2015. SEFE was a one year scientific programme led by Fred Espen Benth and Giulia Di Nunno held at the Centre of Advanced Studies (CAS) in Oslo focussing on the analysis and management of risk in the environmental and financial economics with the aim of first: proposing new mathematical models to describe the uncertain space–time dynamics of weather factors like wind, precipitation and temperature, along with sophisticated models for pricing in energy, commodity, and not least more conventional financial markets and second: to analyse problems of risk management, such as risk evaluation, control, and hedging. During this program the language of stochastic analysis was adopted throughout and both probabilistic and stochastic process methods were used together with stochastic control.

Bernt Øksendal has worked in all the relevant areas within this program, with his most recent years dedicated to risk measurement and control in classical and mean-field setting. This festschrift presents original research contributions in different, relevant areas of SEFE research and in line with Bernt’s interests. The volume is also enriched by the personal introduction: ‘A mathematical journey’, written by Bernt himself.

We are grateful and happy that so many have contributed to this volume and we thank all the authors for their enthusiasm about the project that now reaches fruition. The expert advice of all the referees has been instrumental in producing this issue. We are grateful for their work and their time dedicated to securing the highest standards. We thank all the participants to the conference for their active contribution in the debates during and after the talks. Last but not least, we thank CAS for having provided all the means to organise this conference and for the excellent working conditions during the academic year we spent working on the SEFE programme.

To conclude we happily anticipate enjoying Bernt’s intensive research activity for many more years to come.

All our best wishes, dear Bernt!

Oslo, 29th September 2016

Fred Espen Benth, Giulia Di Nunno, and Saul Jacka