Introductory stochastic analysis for finance and insurance By X. Sheldon Lin, Society of Actuaries
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.
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