Mathematics of the Bond Market: A LÃ vy Processes Approach (Encyclopedia of Mathematics and its Applications, Series Number 174)

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

Michał Barski is Professor of Mathematics at the University of Warsaw. His interests include mathematical finance, especially bond market and risk measures. In the years 2011–2016 he held the position of Junior-Professor in Stochastic Processes and their Applications in Finance at the University of Leipzig.

Jerzy Zabczyk is Professor Emeritus in the Institute of Mathematics at the Polish Academy of Sciences. His research interests include stochastic processes, evolution equations, control theory and mathematical finance. He published over ninety research papers. He is the author or co-author of seven books including Stochastic Equations in Infinite Dimensions (Cambridge, 1992, 2008, 2014), Stochastic Partial Differential Equations with Lévy Noise (Cambridge, 2007) and Mathematical Control Theory: An Introduction (1992, 1996, 2020).