Editorial: Special Issue in memory of Tomas Björk

This Special Issue of Finance and Stochastics celebrates the memory of Tomas Björk who was a leading figure both in the theory of interest rate modelling and in the theory of time-inconsistent stochastic control. He was an Associate Editor of Finance and Stochastics between 1997 and 2011, and the journal was always particularly close to his heart.

Tomas Björk was born on January 08, 1947. He spent his life and academic career in Sweden, travelling widely and presenting his work in many places, and having a big influence on everyone he met. He passed away after a serious illness on January 31, 2021.

On October 10–11, 2022, a conference in memory of Tomas Björk was held in Stockholm at the Swedish House of Finance. After some discussions there, the idea of creating a Special Issue in honour of Tomas was born, and several participants at the conference were happy to contribute. The articles collected here are all connected with Tomas and his work in different ways, and we hope that he would have enjoyed reading them.

The article In memoriam: Tomas Björk (1947–2021). On his career and beyond by Raquel M. Gaspar and Mariana Khapko gives an impression of the many facets and aspects of Tomas, both scientific and personal. Both authors are former PhD students of Tomas, and in their article share their insights into his life, his views and his many contributions.

The article Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments by Yuri Kabanov and Platon Promyslov discusses a question which is close to topics that Tomas studied at the beginning of his career. Later, Yuri Kabanov also worked with Tomas and other colleagues on problems from interest rate theory and made important contributions there.

The article A stochastic control perspective on term structure models with roll-over risk by Claudio Fontana, Simone Pavarana and Wolfgang J. Runggaldier studies a topic which combines two areas of expertise of Tomas: stochastic control theory and the term structure of interest rates. Notably, this work goes beyond the classical paradigm still present in Tomas’ work and addresses multi-curve models as they are needed since the financial crisis.

The article Discount models by Damir Filipović proposes a new parametrisation of interest rate models in terms of so-called discount models. Following ideas developed by Tomas and later Damir Filipović and Josef Teichmann, the article in particular presents a formulation for the arbitrage-free dynamics of a term structure model via a new system of SDEs.

The article Present-biased lobbyists in linear–quadratic stochastic differential games by Ali Lazrak, Hanxiao Wang and Jiongmin Yong picks up on more recent work by Tomas by studying a time-inconsistent game problem with applications in questions about political lobbying in wind energy markets. Like Tomas, Ali Lazrak is a pioneer in studying time-inconsistent optimisation problems and has made significant initial contributions in the area.

The article Robust utility maximisation with intractable claims by Yunhong Li, Zuo Quan Xu and Xun Yu Zhou presents a new utility maximisation problem in a setting where one has to include a contingent claim about which one knows only the probability distribution. This is treated with the help of the so-called quantile formulation which is one of the tools that emerged for non-standard optimisation problems in mathematical finance. Tomas has also worked with Xun Yu Zhou and other colleagues on some aspects of time inconsistency.

The article Asset pricing with dynamically inconsistent agents by Mariana Khapko presents a study of equilibrium and its asset pricing implications in a setting where economic agents have dynamically inconsistent preferences. Mariana Khapko is the last PhD student of Tomas, and this article is a late outgrowth of work she did with Tomas and partly under his supervision.

Finally, the article Thank you, Tomas! by Andrea Gombani gives some very personal impressions of the positive influence Tomas had on the people around him. Andrea Gombani was one of the first to work with Tomas on the term structure of interest rates and played an important role in connecting Tomas to Italy and the mathematical finance activities there.

Tomas always had very high standards of writing and of clarity in expressing ideas. One of his favourite (and most feared) questions was ‘‘What exactly do you mean?’’ All contributors of this Special Issue have worked hard to adhere to Tomas’ standards, and we hope that this collection of articles will stand as a lasting memorial for Tomas and his work.

Martin Schweizer, Editor, Finance and Stochastics September 2023