Advances in Mathematical Finance

by Fu, Michael C.; Jarrow, Robert A.; Yen, Ju-yi J.; Elliott, Robert J.

• ISBN13: 9780817645441
• ISBN10: 0817645446
• Format: Hardcover
• Copyright: 2007-07-30
• Publisher: Birkhauser

Summary

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* Lèvy 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 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

Table of Contents

Preface

Career Highlights and List of Publications

Variance-Gamma & Related Stochastic Processes

The Early Years of the Variance-Gamma Process

Eugene Seneta Variance-Gamma and Monte Carlo

Some Remarkable Properties of Gamma Processes

A Note About Selberg's Integrals in Relation with the Beta-Gamma Algebra

Ito Formulas for Fractional Brownian Motion

Asset & 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 Levy 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 & Investments Beyond Hazard Rates

A New Framework for Credit-Risk Modeling

A Generic One-Factor Levy 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

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