Ebook: An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine
- Tags: Probability Theory and Stochastic Processes, Mathematical Modeling and Industrial Mathematics, Applications of Mathematics, Mathematical Biology in General, Quantitative Finance, Appl.Mathematics/Computational Methods of Engineering
- Series: Modeling and Simulation in Science Engineering and Technology
- Year: 2005
- Publisher: Birkhäuser Boston
- Language: English
- pdf
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.
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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Fundamentals of Probability....Pages 3-50
Stochastic Processes....Pages 51-126
The It? Integral....Pages 127-159
Stochastic Differential Equations....Pages 161-208
Front Matter....Pages 209-209
Applications to Finance and Insurance....Pages 211-238
Applications to Biology and Medicine....Pages 239-279
Back Matter....Pages 281-343
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.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Fundamentals of Probability....Pages 3-50
Stochastic Processes....Pages 51-126
The It? Integral....Pages 127-159
Stochastic Differential Equations....Pages 161-208
Front Matter....Pages 209-209
Applications to Finance and Insurance....Pages 211-238
Applications to Biology and Medicine....Pages 239-279
Back Matter....Pages 281-343
....