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Contents Preliminary Contents. Semi-Martingale Models in Finance: With a Particular Emphasis on Purely Discontinuous Processes (D. Madan). The General Theory of Semi-Martingales (P. Carr, Y. Kabanov and D. Madan). Semi-Martingale Models of the Term Structure (Y. Kabanov). Asset Pricing in Semi-Martingale Models (R. Jarrow). The Generalized Hyperbolic Model (E. Eberlein). The Variance Gamma Model (P. Carr). The CGMY Model (H. Geman). Term Structure Models Driven by Levy Processes (E. Eberlain). Markov Chains of Levy Process Models for Option Calibration (R. Elliot). Time Changed Levy Process for Option Calibration (D. Madan). Hunt Semi-Martingales as Models for Asset Prices (E. Cinlar). Mathematical Results on Levy Processes (M. Yor). Exotic Option Pricing for Vanilla Calibrated Semi-Martingale Models (A. Hirsa).