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Filling a gap in the literature caused by the recent financial crisis, this book provides a treatment of the techniques needed to model and evaluate interest rate derivatives according to the new paradigm for fixed income markets. Concerning this new development, there presently exist only research articles and two books, one of them an edited volume, both being written by researchers working mainly in practice. The aim of this book is to concentrate primarily on the methodological side, thereby providing an overview of the state-of-the-art and also clarifying the link between the new models and the classical literature. The book is intended to serve as a guide for graduate students and researchers as well as practitioners interested in the paradigm change for fixed income markets. A basic knowledge of fixed income markets and related stochastic methodology is assumed as a prerequisite.

Money market. Capital market --- Mathematics --- Quantitative Finance --- Game Theory, Economics, Social and Behav. Sciences --- Game theory --- Economics, Mathematical --- Mathématiques --- Théorie des jeux --- Mathématiques économiques

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Financial Mathematics is an exciting, emerging field of application. The five sets of course notes in this book provide a bird's eye view of the current "state of the art" and directions of research. For graduate students it will therefore serve as an introduction to the field while reseachers will find it a compact source of reference. The reader is expected to have a good knowledge of the basic mathematical tools corresponding to an introductory graduate level, and sufficient familiarity with probabilistic methods, in particular stochastic analysis. B. Biais, J.C. Rochet: Risk-sharing, adverse selection and market structure.- T. Björk: Interest-rate theory.- J. Cvitanic: Optimal trading under constraints.- N. El Karoui, M.C. Quenez: Nonlinear pricing theory and backward stochastic differential equations.- E. Jouini: Market imperfections, equilibrium and arbitrage.

Stochastic processes --- Quantitative methods (economics) --- Business mathematics. --- Business mathematics --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Bedrijfswiskunde --- Mathématiques financières --- Probabilities. --- Public finance. --- Economics, Mathematical . --- Partial differential equations. --- Functional analysis. --- Probability Theory and Stochastic Processes. --- Public Economics. --- Business Mathematics. --- Quantitative Finance. --- Partial Differential Equations. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Economics --- Mathematical economics --- Econometrics --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Cameralistics --- Public finance --- Public finances --- Currency question --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topics are treated in detail: Utility maximization in incomplete markets; the theory of nonlinear expectations and its relationship with the theory of risk measures in a dynamic setting; credit risk modelling; the interplay between finance and insurance; incomplete information in the context of economic equilibrium and insider trading.

Actuarial mathematics --- Finance --- Stochastic analysis --- Mathematical Theory --- Finance - General --- Mathematics --- Business & Economics --- Physical Sciences & Mathematics --- Mathematical models --- Stochastic analysis. --- Finances --- Analyse stochastique --- Mathematical models. --- Modèles mathématiques --- Probabilities. --- Public finance. --- Economics, Mathematical . --- Game theory. --- System theory. --- Probability Theory and Stochastic Processes. --- Public Economics. --- Quantitative Finance. --- Game Theory, Economics, Social and Behav. Sciences. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Games, Theory of --- Theory of games --- Economics --- Mathematical economics --- Econometrics --- Cameralistics --- Public finance --- Public finances --- Currency question --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Philosophy --- Methodology