Description
Book SynopsisThis book provides a concise introduction to stochastic calculus with some of its applications in mathematical finance, engineering and the sciences. Applications in finance include pricing of financial derivatives, such as options on stocks, exotic options and interest rate options. The filtering problem and its solution is presented as an application in engineering. Population models and randomly perturbed equations of physics are given as examples of applications in biology and physics.Only a basic knowledge of calculus and probability is required for reading the book. The text takes the reader from a fairly low technical level to a sophisticated one gradually. Heuristic arguments are often given before precise results are stated, and many ideas are illustrated by worked-out examples. Exercises are provided at the end of chapters to help to test readers' understanding. This book is suitable for advanced undergraduate students, graduate students as well as research workers and practitioners.
Trade Review"It provides a good introduction to stochastic analysis, leaving out several of the more technical proofs. The variety of examples and exercises suggests to use the book for self-studies" Zentralblatt MATH "This book is an excellent introduction to a subject which often presents difficulties to the student of probability ... The numerous exercises are both challenging and illuminating. I greatly enjoyed the book, and can recommend it unreservedly to all probabilists and statisticians wishing to acquire a working knowledge of the stochastic calculus. For libraries, it is an absolute 'must'." Australian & New Zealand Journal of Statistics, 1999 "... the author does a good job at achieving a difficult objective ... the text is best suited for the mathematically inclined graduate student in engineering ... It fills a niche in the literature, as it is hard to find books on stochastic analysis which present such a wide spectrum of results with relatively modest prerequisites." Mathematical Reviews, 2002
Table of ContentsPreliminaries from calculus; concepts of probability theory; basic stochastic processes; Brownian motion calculus; stochastic differential equations; diffusion processes; martingales; calculus for semimartingales; pure jump processes; change of probability measure; applications in finance; applications in biology; applications in engineering and physics.
