This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.
Key topics covered include:
Interacting particles and agent-based models (ant colonies)
Population dynamics: from birth and death processes to epidemics
Financial market models: the non-arbitrage principle
Contingent claim valuation models
Risk analysis in insurance
An Introduction to Continuous-Time Stochastic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, physics, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. TOC:Preface.- Part I: The Theory of Stochastic Processes.- Fundamentals of Probability.- Stochastic Processes.- The Ito Integral.- Stochastic Differential Equations.- Part II: The Applications of Stochastic Processes.- Applications to Finance and Insurance.- Applications to Biology and Medicine.- Part III: Appendices.- A. Measure and Integration.- B. Convergence of Probability Measures on Metric Spaces.- C. Maximum Principles of Elliptic and Parabolic Operators.- D. Stability of Ordinary Differential Equations.- References.
