Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk TheorySpringer Science & Business Media, 10.07.2010 - 376 Seiten Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping. |
Inhalt
| 1 | |
| 11 | |
| 21 | |
| 33 | |
| 43 | |
| 59 | |
| 71 | |
| 106 | |
Itô stochastic integral Itô formula Tanaka formula | 193 |
Stochastic differential equations | 215 |
Optimal stopping of random sequences and processes | 229 |
Measures in a functional spaces Weak convergence probability | 241 |
Statistics of stochastic processes | 271 |
Stochastic processes in financial mathematics discrete time | 303 |
Stochastic processes in financial mathematics continuous time 315 | 314 |
Basic functionals of the risk theory | 327 |
Prediction and interpolation | 129 |
Discrete and continuous time | 137 |
Renewal theory Queueing theory | 159 |
Markov and diffusion processes 175 | 174 |
Appendix | 359 |
Index | 371 |
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Häufige Begriffe und Wortgruppen
arbitrage-free Assume càdlàg call option Chapter characteristic function condition Consider continuous converges covariance function Definition Denote density distribution function dx(t equal exists filtration Find finite finite-dimensional distributions function f H₁ homogeneous i.i.d. random variables independent increments inequality inf{t Itô formula Lebesgue lemma Let X(t Let Xn Markov chain Markov process matrix mean square measure µ metric moment generating function nonnegatively defined orthogonal p_(s P+(s parameter Poisson process previous problem probability space process with independent process with intensity process X(t process X(t),t Prove queue random element random function random sequence random variables random walk request satisfies solution Springer Science+Business Media statement stochastic process submartingale t₁ Theorem trajectories transition function uniformly integrable vector wide-sense stationary Wiener process zero