An Introduction To Continuous- Time Stochastic Processes: Theory, Models, And Applications To Biology, Finance, And Engineering

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, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Key topics covered include:

* Interacting particles and agent-based models: from polymers to ants

* Population dynamics: from birth and death processes to epidemics

* Financial market models: the non-arbitrage principle

* Contingent claim valuation models: the risk-neutral valuation theory

* 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, 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.