Stochastic processes, finance and control : a festschrift in honor of Robert J. Elliott / editors, Samuel N. Cohen [and others].

Includes bibliographical references.

Online resource; title from pdf information screen (Ebsco, viewed June 28, 2013).

Preface; Contents; Stochastic Analysis; 1. On the connection between discrete and continuous Wick calculus with an application to the fractional Black- Scholes model C. Bender and P. Parczewski; 1.1 Introduction; 1.2 Continuous and discrete Wick calculus; 1.2.1. Wiener integrals and Wick exponentials; 1.2.2. Wick product; 1.2.3. Wick powers and Wick-analytic functions; 1.3. Application to the fractional Black-Scholes model; 1.3.1. The fractional Black-Scholes model; 1.3.2. A discrete version of the fractional Black-Scholes market; 1.3.3. Weak convergence to the fractional Black-Scholes model.

1.4. Simulating the discrete version of the fractional Black- Scholes model1.4.1. Discussion of the algorithm; 1.4.2. Numerical results; References; 2. Malliavin differentiability of a class of Feller-diffusions with relevance in Finance C.-O. Ewald, Y. Xiao, Y. Zou and T.K. Siu; 2.1. Introduction; 2.2. Preliminaries on Malliavin calculus; 2.3. Malliavin differentiability of -diffusions; 2.4. Conclusions; Acknowledgments; References; 3. A stochastic integral for adapted and instantly independent stochastic processes H.-H. Kuo, A. Sae-Tang and B. Szozda; 3.1. Introduction.

3.2. Martingales and near-martingales3.3. Near-martingales and the new integral; 3.4. Instantly independent processes and Ito isometry; 3.5. Ito integral and the new integral; 3.6. Further results; References; 4. Independence of some multiple Poisson stochastic integrals with variable-sign kernels N. Privault; 4.1. Introduction; 4.2. Necessary condition for independence; 4.3. Variable-sign kernels; 4.4. Conditional expectations; References; Differential and Stochastic Games; 5. Strategies for differential games W.H. Fleming and D. Hernandez-Hernandez; 5.1. Introduction.

5.2. Differential game formulation5.3. Elliott-Kalton strategies; 5.4. Saddle point property; 5.5. Time discretizations; 5.6. Approximately Markov strategies; 5.7. Progressively measurable strategies; 5.8. Max-plus stochastic control; 5.9. Stochastic differential games; References; 6. BSDE approach to non-zero-sum stochastic differential games of control and stopping I. Karatzas and Q. Li; 6.1. Introduction; 6.1.1. Bibliographic notes; 6.1.2. This paper; 6.2. The games of control and stopping; 6.2.1. The duality between Game and BSDE; 6.2.2. Controls observing volatility.

6.2.3. Rewards terminated by both players6.3. A multi-dimensional reflected BSDE with Lipschitz growth; 6.4. Markovian system with linear growth rate; References; Mathematical Finance; 7. On optimal dividend strategies in insurance with a random time horizon H. Albrecher and S. Thonhauser; 7.1. Introduction and model; 7.2. Exponential time horizon; 7.2.1. Explicit solution in case of exponential claims; 7.3. Erlang time horizon; 7.3.1. State-dependent barrier strategies; 7.3.2. Illustrations; 7.4. Conclusion and outlook; Acknowledgement; References.

8. Counterparty risk and the impact of collateralization in CDS contracts T.R. Bielecki, I. Cialenco and I. Iyigunler.

This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas. This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners.

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