Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective
Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective studies the mathematical issues that arise in modeling the interest rate term structure. These issues are approached by casting the interest rate models as stochastic evolution equations in infinite dimensional function spaces. The book is comprised of three parts. Part I is a crash course on interest rates, including a statistical analysis of the data and an introduction to some popular interest rate models. Part II is a self-contained introduction to infinite dimensional stochastic analysis, including SDE in Hilbert spaces and Malliavin calculus. Part III presents some recent results in interest rate theory, including finite dimensional realizations of HJM models, generalized bond portfolios, and the ergodicity of HJM models.
Investigates interest rate models as stochastic evolution equations in infinite dimensionsThe three parts of the book offer an introduction to interest rates, a review of infinite dimensional stochastic analysis, and recent results in interest rate theoryFirst book to combine infinite dimensional stochastic analysis with Malliavin calculus and interest rate market models