Stochastic differential equations. An introduction with applications. 5th ed. (English) Zbl 0897.60056

Øksendal, Bernt

Universitext. Berlin: Springer. xix, 324 p. (1998).

This is the fifth edition of a highly successful book on stochastic differential equations and related topics. (The earlier editions (1985, 1989, 1992, 1995) are covered by Zbl 0567.60055, Zbl 0694.60046, Zbl 0747.60052 and Zbl 0841.60037, respectively.) In comparison to the fourth edition, there are some minor corrections and improvements and one major change: There is a new chapter (12) which applies the general concepts from stochastic analysis to a financial market model driven by Brownian motions. This chapter presents the key ideas on option pricing in the case of a complete market or more precisely for attainable options. I have no doubt that this edition will meet with the same success as the previous ones.

Reviewer: M.Schweizer (Berlin)

MSC:

60Hxx	Stochastic analysis
60-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60G35	Signal detection and filtering (aspects of stochastic processes)
93E20	Optimal stochastic control
60J60	Diffusion processes
60G40	Stopping times; optimal stopping problems; gambling theory
60J45	Probabilistic potential theory
93E11	Filtering in stochastic control theory

Keywords:

stochastic differential equations; stochastic analysis; financial market; Brownian motions

Citations:

Zbl 0567.60055; Zbl 0694.60046; Zbl 0747.60052; Zbl 0841.60037