Advances in Mathematical Finance

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.

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* Levy process driven fixed-income and credit-risk models, including CDO pricing* Numerical PDE and Monte Carlo methods* Asset pricing and derivatives valuation and hedging* Ito formulas for fractional Brownian motion* Martingale characterization of asset price bubbles* Utility valuation for credit derivatives and portfolio managementAdvances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financialengineering.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

Variance-Gamma and Related Stochastic Processes.- The Early Years of the Variance-Gamma Process.- Variance-Gamma and Monte Carlo.- Some Remarkable Properties of Gamma Processes.- A Note About Selberg’s Integrals in Relation with the Beta-Gamma Algebra.- Itô Formulas for Fractional Brownian Motion.- Asset and Option Pricing.- A Tutorial on Zero Volatility and Option Adjusted Spreads.- Asset Price Bubbles in Complete Markets.- Taxation and Transaction Costs in a General Equilibrium Asset Economy.- Calibration of Lévy Term Structure Models.- Pricing of Swaptions in Affine Term Structures with Stochastic Volatility.- Forward Evolution Equations for Knock-Out Options.- Mean Reversion Versus Random Walk in Oil and Natural Gas Prices.- Credit Risk and Investments.- Beyond Hazard Rates: A New Framework for Credit-Risk Modelling.- A Generic One-Factor Lévy Model for Pricing Synthetic CDOs.- Utility Valuation of Credit Derivatives: Single and Two-Name Cases.- Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model.