Stochastic Analysis with Financial Applications

1. Front Matter

   Pages i-ix

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2. Stochastic Analysis

   1. Front Matter

      Pages 1-1

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   2. Dirichlet Forms for Poisson Measures and Lévy Processes: The Lent Particle Method

      • Nicolas Bouleau, Laurent Denis

      Pages 3-20

   3. Stability of a Nonlinear Equation Related to a Spatially-inhomogeneous Branching Process

      • S. Chakraborty, E. T. Kolkovska, J. A. López-Mimbela

      Pages 21-32

   4. Backward Stochastic Difference Equations with Finite States

      • Samuel N. Cohen, Robert J. Elliott

      Pages 33-42

   5. On a Forward-backward Stochastic System Associated to the Burgers Equation

      • Ana Bela Cruzeiro, Evelina Shamarova

      Pages 43-59

   6. On the Estimate for Commutators in DiPerna–Lions Theory

      • Shizan Fang, Huaiqian Lee

      Pages 61-71

   7. Approximation Theorem for Stochastic Differential Equations Driven by G-Brownian Motion

      • Fuqing Gao, Hui Jiang

      Pages 73-81

   8. Stochastic Flows for Nonlinear SPDEs Driven by Linear Multiplicative Space-time White Noises

      • Benjamin Goldys, Xicheng Zhang

      Pages 83-97

   9. Optimal Stopping Problem Associated with Jump-diffusion Processes

      • Yasushi Ishikawa

      Pages 99-120

   10. A Review of Recent Results on Approximation of Solutions of Stochastic Differential Equations

       • Benjamin Jourdain, Arturo Kohatsu-Higa

       Pages 121-144

   11. Strong Consistency of Bayesian Estimator Under Discrete Observations and Unknown Transition Density

       • Arturo Kohatsu-Higa, Nicolas Vayatis, Kazuhiro Yasuda

       Pages 145-167

   12. Exponentially Stable Stationary Solutions for Delay Stochastic Evolution Equations

       • Jiaowan Luo

       Pages 169-178

   13. Robust Stochastic Control and Equivalent Martingale Measures

       • Bernt Øksendal, Agnès Sulem

       Pages 179-189

   14. Multi-valued Stochastic Differential Equations Driven by Poisson Point Processes

       • Jiagang Ren, Jing Wu

       Pages 191-205

   15. Sensitivity Analysis for Jump Processes

       • Atsushi Takeuchi

       Pages 207-219

   16. Quantifying Model Uncertainties in Complex Systems

       • Jiarui Yang, Jinqiao Duan

       Pages 221-252

3. Financial Applications

   1. Front Matter

      Pages 253-253

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   2. Convertible Bonds in a Defaultable Diffusion Model

      • Tomasz R. Bielecki, Stéphane Crépey, Monique Jeanblanc, Marek Rutkowski

      Pages 255-298

   3. A Convexity Approach to Option Pricing with Transaction Costs in Discrete Models

      • Tzuu-Shuh Chiang, Shuenn-Jyi Sheu

      Pages 299-315

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

• quantitative finance

• Japan Science and Technology Agency, Department of Mathematical Sciences, Ritsumeikan University, Shiga, Japan

  Arturo Kohatsu-Higa

• Division of Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

  Nicolas Privault

• Department of Mathematics, National Central University, Zhongli City, Taiwan R.O.C.

  Shuenn-Jyi Sheu

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