Synopses & Reviews
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday. Specific topics covered include: * Theory and application of the Variance-Gamma process * Lévy process driven fixed-income and credit-risk models, including CDO pricing * Numerical PDE and Monte Carlo methods * Asset pricing and derivatives valuation and hedging * Itô formulas for fractional Brownian motion * Martingale characterization of asset price bubbles * Utility valuation for credit derivatives and portfolio management Advances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering. Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou
Synopsis
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with s- ni?cant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the int- leaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?o- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilizationwith diverse areas. The intricate and f- damental relationship between harmonic analysis and ?elds such as signal processing, partial di?erential equations (PDEs), and image processing is - ?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.
Synopsis
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
Table of Contents
ANHA Series Preface
Preface
Career Highlights and List of Publications / Dilip B. Madan
Part I. Variance-Gamma and Related Stochastic Processes
The Early Years of the Variance-Gamma Process / Eugene Seneta
Variance-Gamma and Monte Carlo / Michael C. Fu
Some Remarkable Properties of Gamma Processes / Marc Yor
A Note About Selberg's Integrals in Relation with the Beta-Gamma Algebra / Marc Yor
Itô Formulas for Fractional Brownian Motion / Robert J. Elliott and John van der Hoek
Part II. Asset and Option Pricing
A Tutorial on Zero Volatility and Option Adjusted Spreads / Robert A. Jarrow
Asset Price Bubbles in Complete Markets / Robert A. Jarrow, Philip Protter, and Kazuhiro Shimbo
Taxation and Transaction Costs in a General Equilibrium Asset Economy / Xing Jin and Frank Milne
Calibration of Lévy Term Structure Models / Ernst Eberlein and Wolfgang Kluge
Pricing of Swaptions in Affine Term Structures with Stochastic Volatility / Massoud Heidari, Ali Hirsa, and Dilip B. Madan
Forward Evolution Equations for Knock-Out Options / Peter Carr and Ali Hirsa
Mean Reversion Versus Random Walk in Oil and Natural Gas Prices / Hélyette Geman
Part III. Credit Risk and Investments
Beyond Hazard Rates: A New Framework for Credit-Risk Modelling / Dorje C. Brody, Lane P. Hughston, and Andrea Macrina
A Generic One-Factor Lévy Model for Pricing Synthetic CDOs / Hansjörg Albrecher, Sophie A. Ladoucette, and Wim Schoutens
Utility Valuation of Credit Derivatives: Single and Two-Name Cases / Ronnie Sircar and Thaleia Zariphopoulou
Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model / Marek Musiela and Thaleia Zariphopoulou