CONTENTS -- Preface -- Program -- Financial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy S. Ankirchner and P. Imkell -- 1. Introduction -- 2. Additional Logarithmic Utility and Information Drift -- 3. The Information Drift and the Law of Additional Information -- 4. Additional Utility and Entropy of Filtrations -- References -- A Localization of the Levy Operators Arising in Mathematical Finances M. Arisawa -- 1. Introduction -- 2. Comparison Results -- 3. Uniform Hölder Continuities of Viscosity Solutions -- 4. Other Hölder Continuities of Viscosity Solutions -- 5. Strong Maximum Principle -- 6. Ergodic Problem for Integro-di.erential Equations -- References -- Model-free Representation of Pricing Rules as Conditional Expectations S. Biagini and R. Cont -- 1. Introduction -- 1.1 Model-based vs model-free arbitrage -- 2. Definitions and Notations -- 3. Pricing Rules as Conditional Expectation Operators -- 4. Discussion -- 4.1 Implications for the specification of derivative pricing models -- 4.2 The domain of the pricing rule -- 4.3 Introduction of a set of benchmark assets -- References -- A Class of Financial Products and Models Where Super-replication Prices are Explicit L. Carassus, E. Gobet, and E. Temam -- 1. Introduction -- 2. The Financial Model and Super-replication Theorem -- 2.1 Notations and definitions -- 2.2 Super-replication Theorem -- 3. The Main Results -- 4. Application: Some Super-replication Prices -- 4.1 Specification of the models -- 4.2 Computation of the prices in dimension one -- 4.2.1 Vanilla Options. -- 4.2.2 Barrier Options. -- 4.2.3 Extension. -- 5. Conclusion -- Appendix: Proof of Theorem 2.2 -- References -- Risky Debt and Optimal Coupon Policy and Other Optimal Strategies D. Dorobantu and M. Pontier -- 1. Introduction -- 1.1 Optimal stopping tools -- 2. A simple model.

2.1 Mixed Brownian-Poisson process diffusion -- 2.2 Optimal stopping problem -- 2.3 Function φ -- 3. Reflective diffusion -- 4. Conclusion -- References -- Affine Credit Risk Models under Incomplete Information R. Frey, C. Prosdocimi, and W. J. Runggaldier -- 1. Introduction -- 2. The Model and Some Basic Examples -- 2.1 The affine case -- 2.2 Examples -- 2.2.1 Example 1. Defaultable zero-coupon bond on firm j with maturity T and zero recovery -- 2.2.2 Example 2. Recovery payment -- 2.2.3 Example 3. Survival probabilities -- 3. Incomplete Information (The Filtering Problem) -- 3.1 The filtering problem -- 3.2 General solution of the filtering problem -- 3.2.1 Filter between defaults -- 3.2.2 Filter at a default -- 4. Filtering in Affine Models -- 4.1 Filter between defaults -- 4.2 Filter at a default time -- 4.3 Filter algorithm -- 5. Finite Dimensional Computation of the Filter -- References -- Smooth Rough Paths and the Applications K. Hara and T. Lyons -- 1. Introduction -- 2. Definitions -- 3. Main Results -- 4. Applications -- 5. Related Problems -- 5.1 When is the rough path property preserved? -- 5.2 automatic rough paths -- 5.3 probabilistic versions of the First Theorem -- References -- From Access to Bypass: A Real Options Approach K. Hori and K. Mizuno -- 1. Introduction -- 2. The Model -- 2.1 Production in a network industry under imperfect competition -- 2.2 A two-firm case -- 3. Three Benchmarks -- 3.1 Simultaneous investment -- 3.2 Bypass equilibrium -- 3.3 Access equilibrium -- 4. The Access-to-Bypass Equilibrium -- 4.1 Possible equilibria under open access policy -- 4.2 A follower's choice of strategy -- 4.3 A leader's firm value -- 4.4 The equilibrium -- 5. The E.ects of Open Access Policy -- 5.1 Equilibria in service-based and facility-based competitions -- 5.2 The e.ect on a follower's entry timing.

5.3 The e.ect on a leader's entry timing -- 6. Uncertainty's e.ect on the choice of competition regimes -- 7. Concluding Remarks -- Appendix The derivation of a single firm's value function in the case of simultaneous investment -- References -- The Investment Game under Uncertainty: An Analysis of Equilibrium Values in the Presence of First or Second Mover Advantage J. Imai and T.Watanabe -- 1. Introduction -- 2. Model Description -- 2.1 A Basic Mode -- 2.2 Derivation of the Project Values -- 3. Numerical experiences and economical implication -- 3.1 Selection of parameters -- 3.2 Project values under the condition of FMA -- 3.3 Project values under the condition of SMA -- 3.4 Discontinuity between FMA and SMA -- 4. Concluding Remarks -- References -- Asian Strike Options of American Type and Game Type M. Ishihara and H. Kunita -- 1. Introduction -- 2. Average Strike Put Options -- 3. American Average Strike Put Options -- 4. Average Strike Put Options of the Game Type -- 5. Early Exercise Premium and Early Cancellation Fee -- 6. Appendix: A Generalized Ito's Formula and Local Time of a One Dimensional Stochastic Flow -- References -- Minimal Variance Martingale Measures for Geometric Levy Processes M. Jeanblanc, S. Kloeppel, and Y. Miyahara -- 1. Problems and Results -- 2. Remarks -- References -- Cubature on Wiener Space Continued C. Litterer and T. Lyons -- 1. Introduction -- 2. Higher order methods for weak approximations of SDEs -- 3. High order recombination for evolving stochastic systems -- 4. A measure support reduction algorithm -- 5. A second algorithm -- 6. Some results from cubature onWiener space -- 7. Cubature with recombination -- 8. Application of the recombination methods to the stochastic filtering problem -- References -- A Remark on Impulse Control Problems with Risk-sensitive Criteria H. Nagai -- 1. Introduction.

2. A Verification Theorem -- References -- A Convolution Approach to Multivariate Bessel Proceses T. V. Nguyen, S. Ogawa, and M. Yamazato -- 1. Introduction and Prelimilaries -- 2. The Cartersian Product of Kingman Convolution Algebras -- 3. Multivariate Symmetric RandomWalks -- References -- Spectral Representation of Multiply Self-decomposable Stochastic Processes and Applications N. V. Thu, T. A. Dung, D. T. Dam, and N. H. Thai -- 1. Introduction, Notation and Preliminaries -- 2. Mappings {T(α) c } and Classes {Lα(X)} -- 2.1 α = n = 1, 2, ... -- 2.3 The general case α > 0 : -- 3. Mappings {U(α) c } and Classes {Uα(X)} -- 4. Stochastic Representation of MSDPM's and s-MSDPM's. -- 5. An Application in Option Pricing -- References -- Stochastic Growth Models of an Isolated Economy K. Nishioka -- 1. Introduction -- 2. Verification of Solow model -- 3. The stochastic Solow equation -- 4. A quaere to Inada condition -- References -- Numerical Approximation by Quantization for Optimization Problems in Finance under Partial Observations H. Pham -- 1. Introduction -- 2. Partial Observation Discrete-time Framework -- 2.1 Signal-observation model -- 2.2 Filter evolution -- 3. Dynamic Optimization Models -- 3.1 Optimal stopping -- 3.2 Control problems -- 4. Short Background on Optimal Vector Quantization -- 5. Quantization of the Filter Process -- 6. Numerical Approximation to Optimization Problems under Partial Observation -- 6.1 Quantization of optimal stopping -- References.