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 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

Includes contributions from some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering Offers state-of-the-art developments in theory and practice Real-world applications to fixed-income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium Ideal for a broad audience of graduate students, researchers, and practitioners in mathematical finance and financial engineering Suitable for readers coming from academia as well as industry

Zusammenfassung
Includes a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting the developments in theory and practice, this book offers applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium.

Inhalt
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.