Kirjahaku

Stochastic di?erential equations model stochastic evolution as time evolves. These models have a variety of applications in many disciplines and emerge naturally in the study of many phenomena. Examples of these applications are physics (see, e. g. , [176] for a review), astronomy [202], mechanics [147], economics [26], mathematical ?nance [115], geology [69], genetic analysis (see, e. g. , [110], [132], and [155]), ecology [111], cognitive psychology (see, e. g. , [102], and [221]), neurology [109], biology [194], biomedical sciences [20], epidemi- ogy [17], political analysis and social processes [55], and many other ?elds of science and engineering. Although stochastic di?erential equations are quite popular models in the above-mentioned disciplines, there is a lot of mathem- ics behind them that is usually not trivial and for which details are not known to practitioners or experts of other ?elds. In order to make this book useful to a wider audience, we decided to keep the mathematical level of the book su?ciently low and often rely on heuristic arguments to stress the underlying ideas of the concepts introduced rather than insist on technical details. Ma- ematically oriented readers may ?nd this approach inconvenient, but detailed references are always given in the text. As the title of the book mentions, the aim of the book is twofold.

Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.

Stochastic di?erential equations model stochastic evolution as time evolves. These models have a variety of applications in many disciplines and emerge naturally in the study of many phenomena. Examples of these applications are physics (see, e. g. , [176] for a review), astronomy [202], mechanics [147], economics [26], mathematical ?nance [115], geology [69], genetic analysis (see, e. g. , [110], [132], and [155]), ecology [111], cognitive psychology (see, e. g. , [102], and [221]), neurology [109], biology [194], biomedical sciences [20], epidemi- ogy [17], political analysis and social processes [55], and many other ?elds of science and engineering. Although stochastic di?erential equations are quite popular models in the above-mentioned disciplines, there is a lot of mathem- ics behind them that is usually not trivial and for which details are not known to practitioners or experts of other ?elds. In order to make this book useful to a wider audience, we decided to keep the mathematical level of the book su?ciently low and often rely on heuristic arguments to stress the underlying ideas of the concepts introduced rather than insist on technical details. Ma- ematically oriented readers may ?nd this approach inconvenient, but detailed references are always given in the text. As the title of the book mentions, the aim of the book is twofold.