An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine (Modeling and Simulation in Science, Engineering and Technology) - Hardcover

Capasso, Vincenzo; Bakstein, David

Hardcover

ISBN 10: 0817632344 ISBN 13: 9780817632342

Verlag: Birkhäuser, 2004

Inhaltsangabe

This book is a systematic, rigorous, and self-consistent introduction to the theory of continuous-time stochastic processes. But it is neither a tract nor a recipe book as such; rather, it is an account of fundamental concepts as they appear in relevant modern applications and literature. We make no pretense of it being complete. Indeed, we have omitted many results, which we feel are notdirectly relatedtothemain themeorthatare availablein easilyaccessible sources. (Thosereaderswhoareinterestedinthehistoricaldevelopmentofthe subject cannot ignore the volume edited by Wax (1954). ) Proofs are often omitted as technicalities might distract the reader from a conceptual approach. They are produced whenever they may serve as a guide to the introduction of new concepts and methods towards the app- cations; otherwise, explicit references to standard literature are provided. A mathematically oriented student may ?nd it interesting to consider proofs as exercises. The scope of the book is profoundly educational, related to modeling re- world problems with stochastic methods. The reader becomes critically aware oftheconceptsinvolvedincurrentappliedliterature,andismoreoverprovided with a ?rm foundation of the mathematical techniques. Intuition is always supported by mathematical rigor. Our book addresses three main groups: ?rst, mathematicians working in a di?erent ?eld; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications.

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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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 0817632344
• ISBN 13: 9780817632342
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 358
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar