Time-Inconsistent Control Theory with Finance Applications

Tomas Björk was a Professor of Mathematical Finance at the Stockholm School of Economics. He was also affiliated with KTH (Royal Institute of Technology), Sweden, and Aarhus University, Denmark. Tomas served as president of the Bachelier Finance Society, co-editor of the journal Mathematical Finance, and a member of the editorial board of Finance and Stochastics and other journals. He published numerous journal articles on mathematical finance, and in particular is known for his research on point process driven forward-rate models, consistent forward-rate curves, general interest-rate theory, finite-dimensional realizations of infinite-dimensional SDEs, good deal bounds, and time-inconsistent control theory. Tomas was the author of the widely used and influential textbook, Arbitrage Theory in Continuous Time, which is now in its fourth edition. He passed away in 2021. Mariana Khapko is an Assistant Professor of Finance at the University of Toronto,Canada. She is also an affiliated Research Fellow of the Swedish House of Finance at the Stockholm School of Economics. Her research focuses on financial mathematics and financial markets. She has published articles on time-inconsistent control theory, asset pricing and portfolio choice, information in securities markets, and financial market design. Mariana obtained her PhD in Finance from the Stockholm School of Economics, under the supervision of Tomas Björk.Agatha Murgoci currently works as a senior quantitative developer at Ørsted, a leading off-shore wind energy company. Prior to this, she was an assistant professor at Copenhagen Business School and at Aarhus University, Denmark. She has published papers on time-inconsistent control theory, good deal bounds, convexity corrections, and the dynamics of sovereign and bank CDS spreads. Agatha obtained her PhD in Mathematical Finance from the Stockholm School of Economics, under the supervision of Tomas Björk.

“The book represents a very valuable contribution to the literature and will surely make the theory of time-inconsistent stochastic control known to a large audience.” (Claudio Fontana, zbMATH 1491.91003, 2022)

• 1 Introduction.- Part I Optimal Control in Discrete Time.- 2 Dynamic Programming Theory.- 3 The Linear Quadratic Regulator.- 4 A Simple Equilibrium Model.- Part II Time-Inconsistent Control in Discrete Time.- 5 Time-Inconsistent Control Theory.- 6 Extensions and Further Results.- 7 Non-Exponential Discounting.- 8 Mean-Variance Portfolios.- 9 Time-Inconsistent Regulator Problems.- 10 A Time-Inconsistent Equilibrium Model.- Part III Optimal Control in Continuous Time.- 11 Dynamic Programming Theory.- 12 The Continuous-Time Linear Quadratic Regulator.- 13 Optimal Consumption and Investment.- 14 A Simple Equilibrium Model.- Part IV Time-Inconsistent Control in Continuous Time.- 15 Time-Inconsistent Control Theory.- 16 Special Cases and Extensions.- 17 Non-Exponential Discounting.- 18 Mean-Variance Control.- 19 The Inconsistent Linear Quadratic Regulator.- 20 A Time-Inconsistent Equilibrium Model.- Part V Optimal Stopping Theory.- 21 Optimal Stopping in Discrete Time.- 22 Optimal Stopping in Continuous Time.- Part VI Time-Inconsistent Stopping Problems.- 23 Time-Inconsistent Stopping in Discrete Time.- 24 Time-Inconsistent Stopping in Continuous Time.- 25 Time-Inconsistent Stopping Under Distorted Probabilities.- A Basic Arbitrage Theory.- References.