Introductory Stochastic Analysis for Finance and Insurance

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.

Auteur
X. SHELDON LIN, PhD, ASA, is Professor of Actuarial Sciences in the Department of Statistics, University of Toronto. He is an Associate of the Society of Actuaries and an Associate Editor for North American Actuarial Journal and Insurance: Mathematics and Economics. Dr. Lin's research interests include mathematical finance, actuarial science, and applied probability. He is an author or coauthor of more than 40 research papers in these areas. He jointly received two annual prizes of the Society of Actuaries in 1998 and 2004 for his research in actuarial science.

Résumé
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.

Contenu
List of Figures. List of Tables.

Preface.

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.

References.

Topic Index.