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Introductory Stochastic Analysis for Finance and Insurance

X. Sheldon Lin, Society of Actuaries

ISBN: 978-0-471-79321-2 April 2006 224 Pages


Incorporates the many tools needed for modeling and pricing in finance and insurance

Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory.

Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers.

This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested. Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries:
* Overview of Probability Theory
* Discrete-Time stochastic processes
* Continuous-time stochastic processes
* Stochastic calculus: basic topics

The final two chapters, Stochastic Calculus: Advanced Topics and Applications in Insurance, are devoted to more advanced topics. Readers learn the Feynman-Kac formula, the Girsanov's theorem, and complex barrier hitting times distributions. Finally, readers discover how stochastic analysis and principles are applied in practice through two insurance examples: valuation of equity-linked annuities under a stochastic interest rate environment and calculation of reserves for universal life insurance.

Throughout the text, figures and tables are used to help simplify complex theory and pro-cesses. An extensive bibliography opens up additional avenues of research to specialized topics.

Ideal for upper-level undergraduate and graduate students, this text is recommended for one-semester courses in stochastic finance and calculus. It is also recommended as a study guide for professionals taking Causality Actuarial Society (CAS) and Society of Actuaries (SOA) actuarial examinations.
List of Figures.

List of Tables.


1. Introduction.

2. Overview of Probability Theory.

3. Discrete-Time Stochastic Processes.

4. Continuous-Time Stochastic Processes.

5. Stochastic Calculus: Basic Topics.

6. Stochastic Calculus: Advanced Topics.

7. Applications in Insurance.


Topic Index.

"…a positive addition to the introductory textbooks on stochastic calculus for financial applications." (Journal of the American Statistical Association, June 2007)

"The actuarial topics discussed by the author are absolutely nonstandard and provide a strong point in favor of this book compared to its competitors…" (Mathematical Reviews, Issue 2007a)

"…very suitable for practitioners who just need to understand the main connections between some financial concepts and stochastic analysis." (MAA Reviews, April 30, 2006)

  •  It has been class-tested extensively in a variety of financial environments.
  • It is written at a level which is friendly to actuaries, i.e. devoid of heavy proofs. 
  •  There is an extensive bibliography at the rear of the book that serves as a primary source for new and timely publications in a constantly changing, dynamic marketplace.
  • The last two chapters are devoted to advanced topics, such as the Feynman-Kac Formula, the Girsanov Theorem and complex barrier hitting times and two specific insurance applications, valuation of an equity-indexed annuity under a stochastic interest rate environment and calculated reserve for Universal Life. 
  •  Unlike most introductory texts in probability theory, attention is paid to:
    1.  the notion of information structure and how it relates to a probability space and a random variable.
    2.  the notion of conditional probability and conditional expectation, and their respective calculations.