Contents -- Preface -- Contributors and Addresses -- PART I STOCHASTIC ANALYSIS AND SYSTEMS -- Multidimensional Wick-Itô Formula for Gaussian Processes -- 1. Introduction -- 2. Preliminaries -- 3. Main Result -- 4. Technical Lemmas -- 5. Convergence Results -- 6. Examples -- 6.1. Correlated Heterogeneous Fractional Brownian Motion -- 6.2. Multidimensional Fractional Brownian Motion -- 7. Application to the Pricing of an Exchange Option -- References -- Fractional White Noise Multiplication -- 1. Introduction -- 2. Fractional Integral Representation of Fractional Brownian Motion -- 3. Fractional Differential Operator -- 4. Fractional White Noise Multiplication -- 5. A Binomial-Type Finance Model -- References -- Invariance Principle of Regime-Switching Diffusions -- 1. Introduction -- 1.1. Introduction -- 1.2. Our Contributions -- 1.3. Applications to Mathematical Finance -- 1.4. Outline -- 2. Formulation -- 3. Main Results -- 4. Further Remarks -- Acknowledgments -- References -- PART II FINANCE AND STOCHASTICS -- Real Options and Competition -- 1. Introduction -- 2. Valuation and General Features of Problems and Models -- 2.1. Asset Valuation in Complete and Incomplete Markets -- 2.2. Market Frameworks -- 2.3. Types of Investment Payoffs -- 3. The Complete Market Case -- 3.1. Single Player -- 3.2. Two Players: A Stackelberg Leader-Follower Game -- 4. The Incomplete Market Case -- 4.1. Utility-Based Pricing -- 4.2. Single Player -- 4.3. Two Players: A Stackelberg Leader-Follower Game -- 5. Conclusion -- References -- Finding Expectations of Monotone Functions of Binary Random Variables by Simulation, with Applications to Reliability, Finance, and Round Robin Tournaments -- 1. Introduction -- 2. Estimating E[ϕ(X1, . . . ,Xn)] by Simulation -- 3. Monotonicity of the Conditional Expectation Given T -- 4. The Classical Reliability Model.

5. A Dynamic Reliability Model -- 6. Modeling Basket Default Costs -- 7. A Round Robin Tournament -- Acknowledgments -- References -- Filtering with Counting Process Observations and Other Factors: Applications to Bond Price Tick Data -- 1. Introduction -- 2. The Simple FM Model with an Observable Factor -- 2.1. Representation I: Constructing Price from Intrinsic Value -- 2.2. Filtering with Counting Process Observations -- 2.3. The Equivalence of the Two Representation -- 3. Bayes Estimation via Filtering -- 3.1. The Statistical Foundations -- 3.2. Filtering Equations -- 3.3. A Convergence Theorem and Recursive Algorithms -- 3.4. The Recursive Algorithms for Posteriors and Bayes Estimates -- 4. A Monte Carlo Example -- 4.1. Tick Characteristics of Monte Carlo Data -- 4.2. Bayes Estimates for Monte Carlo Data -- 5. An Empirical Study of 5-year Treasury Note -- 6. Conclusion -- Appendix A. More on Clustering Noise -- Acknowledgments -- References -- Jump Bond Markets Some Steps towards General Models in Applications to Hedging and Utility Problems -- 1. Preliminaries: The Basic Model -- 2. MVH in Jump Bond Markets -- 2.1. Hedging on the Basis of n Maturity Times and the Variance Optimal Martingale Measure -- 2.2. ε*-Martingale and Mean-Variance Hedging -- 2.3. The Case of not Invertible S -- 3. Optimal Exponential Utility in Jump Bond Markets -- 3.1. The Minimal Entropy Martingale Based on [T0, T*] -- 3.2. The Locally Square Integrable (LSI) Cylindrical Martingales and the Normalized Martingale -- 3.3. The Dynamics of the MEM Based on [T0, T*] -- 3.4. An Example -- 3.5. Optimal Exponential Utility -- 3.6. The Dynamic Exp Utility Indifference Valuation -- 4. Outlook -- References -- Recombining Tree for Regime-Switching Model: Algorithm and Weak Convergence -- 1. Introduction -- 2. Regime-Switching Trees and Option Pricing.

2.1. Regime-Switching Model -- 2.2. A Direct Extension of CRR Tree to Regime-Switching -- 2.3. A Regime-Switching Recombining Tree -- 3. Convergence of the Tree Approximations -- 4. Concluding Remarks -- References -- Optimal Reinsurance under a Jump Diffusion Model -- 1. Introduction -- 2. Formulation and HJB Equation -- 3. Solution to the HJB Equation -- 4. Special Claim Distributions -- 4.1. The Case with Exponential Claims -- 4.2. The Case with Gamma Claims -- 4.3. Numerical Examples -- Acknowledgments -- References -- Applications of Counting Processes and Martingales in Survival Analysis -- 1. Introduction -- 2. Regression Analysis of Right-censored Failure Time Data Using the Cox Model -- 3. Regression Analysis of Current Status Failure Time Data Using the Additive Hazards Model -- 3.1. Current Status Failure Time Data -- 3.2. Regression Analysis using the Additive Hazards Model -- 4. Regression Analysis of Bivariate Current Status Failure Time Data Using the Cox Model -- 4.1. Assumptions and the Likelihood Function -- 4.2. Efficient Estimation of Regression Parameters -- 5. Concluding Remarks -- References -- Stochastic Algorithms and Numerics for Mean-Reverting Asset Trading -- 1. Introduction -- 2. Problem Formulation -- 3. Convergence and Rates of Convergence -- 4. Numerical Demonstration -- 4.1. Simulation Study -- 4.2. Tests with Market Data -- 5. Further Remarks -- References.