An Introduction to Continuous-Time Stochastic Processes [electronic resource] : Theory, Models, and Applications to Finance, Biology, and Medicine / by Vincenzo Capasso, David Bakstein.
Contributor(s): Bakstein, David [author.] | SpringerLink (Online service)Material type: TextSeries: Modeling and Simulation in Science, Engineering and Technology: Publisher: Boston, MA : Birkhäuser Boston, 2005Description: XIV, 344 p. 13 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817644284Subject(s): Mathematics | Applied mathematics | Engineering mathematics | Economics, Mathematical | Mathematical models | Probabilities | Biomathematics | Mathematics | Applications of Mathematics | Probability Theory and Stochastic Processes | Mathematical Modeling and Industrial Mathematics | Mathematical and Computational Biology | Quantitative Finance | Appl.Mathematics/Computational Methods of EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: T57-57.97Online resources: Click here to access online
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The Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- The Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine.
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.