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

Contenu
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.