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Basic Stochastic Processes.
This book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fai...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2015.
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| Colección: | Mathematics and statistics series (ISTE)
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Contents; Introduction; 1: Basic Probabilistic Tools for Stochastic Modeling; 1.1. Probability space and random variables; 1.2. Expectation and independence; 1.3. Main distribution probabilities; 1.3.1. Binomial distribution; 1.3.2. Negative exponential distribution; 1.3.3. Normal (or Laplace-Gauss) distribution; 1.3.4. Poisson distribution; 1.3.5. Lognormal distribution; 1.3.6. Gamma distribution; 1.3.7. Pareto distribution; 1.3.8. Uniform distribution; 1.3.9. Gumbel distribution; 1.3.10. Weibull distribution; 1.3.11. Multi-dimensional normal distribution.
- 1.3.12. Extreme value distribution1.3.12.1. Definition; 1.3.12.2. Asymptotic results; 1.3.12.3. Exact values of the norming constants; 1.3.12.4. Parameters estimation [ESC 97]; 1.3.12.5. Characteristic of extreme value distribution; 1.4. The normal power (NP) approximation; 1.5. Conditioning; 1.6. Stochastic processes; 1.7. Martingales; 2: Homogeneous and Non-homogeneous Renewal Models; 2.1. Introduction; 2.2. Continuous time non-homogeneous convolutions; 2.2.1. Non-homogeneous convolution product; 2.3. Homogeneous and non-homogeneous renewal processes.
- 2.4. Counting processes and renewal functions2.5. Asymptotical results in the homogeneous case; 2.6. Recurrence times in the homogeneous case; 2.7. Particular case: the Poisson process; 2.7.1. Homogeneous case; 2.7.2. Non-homogeneous case; 2.8. Homogeneous alternating renewal processes; 2.9. Solution of non-homogeneous discrete time evolution equation; 2.9.1. General method; 2.9.2. Some particular formulas; 2.9.3. Relations between discrete time and continuous time renewal equations; 3: Markov Chains; 3.1. Definitions; 3.2. Homogeneous case; 3.2.1. Basic definitions.
- 3.2.2. Markov chain state classification3.2.3. Computation of absorption probabilities; 3.2.4. Asymptotic behavior; 3.2.5. Example: a management problem in an insurance company; 3.3. Non-homogeneous Markov chains; 3.3.1. Definitions; 3.3.2. Asymptotical results; 3.4. Markov reward processes; 3.4.1. Classification and notation; 3.4.1.1. Classification of reward processes; 3.4.1.2. Financial parameters; 3.5. Discrete time Markov reward processes (DTMRWPs); 3.5.1. Undiscounted case; 3.5.1.1. First model; 3.5.1.2. Second model; 3.5.1.3. Third model; 3.5.1.4. Fourth model; 3.5.2. Discounted case.
- 3.5.2.1. Immediate cases3.5.2.1.1. First model; 3.5.2.1.2. Second model; 3.5.2.1.3. Third model; 3.5.2.1.4. Fourth model; 3.5.2.1.5. Fifth model; 3.5.2.1.6. Sixth model; 3.5.2.2. Due cases; 3.5.2.2.1. First model; 3.5.2.2.2. Second model; 3.5.2.2.3. Third model; 3.5.2.2.4. Fourth model; 3.6. General algorithms for the DTMRWP; 3.6.1. Homogeneous MRWP; 3.6.2. Non-homogeneous MRWP; 4: Homogeneous and Non-homogeneous Semi-Markov Models; 4.1. Continuous time semi-Markov processes; 4.2. The embedded Markov chain; 4.3. The counting processes and the associated semi-Markov process.