Theory of Stochastic Processes With Applications to Financial Mathematics and Risk Theory /
This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory. The aim of this book is to provide the reader with the theoretical and practical material...
| Main Authors: | , , , , |
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| Corporate Author: | |
| Format: | Electronic |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
2010.
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| Series: | Problem Books in Mathematics,
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| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-87862-1 |
Table of Contents:
- Preface
- Definition of stochastic process. Cylinder s -algebra, finitedimensional distributions, the Kolmogorov theorem
- Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions
- Trajectories. Modifications. Filtrations
- Continuity. Differentiability. Integrability
- Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures
- Gaussian processes
- Martingales and related processes in discrete and continuous time. Stopping times
- Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values
- Prediction and interpolation
- Markov chains: Discrete and continuous time
- Renewal theory. Queueing theory
- Markov and diffusion processes
- Itŏ stochastic integral. Itŏ formula. Tanaka formula
- Stochastic differential equations
- Optimal stopping of random sequences and processes
- Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems
- Statistics of stochastic processes
- Stochastic processes in financial mathematics (discrete time)
- Stochastic processes in financial mathematics (continuous time)
- Basic functionals of the risk theory
- Appendix
- Index.