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Stochastic processes for insurance and finance [[electronic resource] /] / Tomasz Rolski ... [et al.]
| Stochastic processes for insurance and finance [[electronic resource] /] / Tomasz Rolski ... [et al.] |
| Pubbl/distr/stampa | Chicester, : J. Wiley, 1999 |
| Descrizione fisica | 1 online resource (683 p.) |
| Disciplina |
332
368.015192 |
| Altri autori (Persone) | RolskiTomasz |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Insurance - Mathematical models
Finance - Mathematical models Stochastic processes |
| ISBN |
9786612307928
0-470-31788-4 1-282-30792-4 0-470-86042-1 0-470-31704-3 0-585-27223-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Stochastic Processes for Insurance and Finance; Contents; Preface; List of Principal Notation; 1 Concepts from Insurance and Finance; 1.1 Introduction; 1.2 The Claim Number Process; 1.2.1 Renewal Processes; 1.2.2 Mixed Poisson Processes; 1.2.3 Some Other Models; 1.3 The Claim Size Process; 1.3.1 Dangerous Risks; 1.3.2 The Aggregate Claim Amount; 1.3.3 Comparison of Risks; 1.4 Solvability of the Portfolio; 1.4.1 Premiums; 1.4.2 The Risk Reserve; 1.4.3 Economic Environment; 1.5 Reinsurance; 1.5.1 Need for Reinsurance; 1.5.2 Types of Reinsurance; 1.6 Ruin Problems; 1.7 Related Financial Topics
1.7.1 Investment of Surplus1.7.2 Diffusion Processes; 1.7.3 Equity Linked Life Insurance; 2 Probability Distributions; 2.1 Random Variables and Their Characteristics; 2.1.1 Distributions of Random Variables; 2.1.2 Basic Characteristics; 2.1.3 Independence and Conditioning; 2.1.4 Convolution; 2.1.5 Transforms; 2.2 Parametrized Families of Distributions; 2.2.1 Discrete Distributions; 2.2.2 Absolutely Continuous Distributions; 2.2.3 Parametrized Distributions with Heavy Tail; 2.2.4 Operations on Distributions; 2.2.5 Some Special Functions; 2.3 Associated Distributions 2.4 Distributions with Monotone Hazard Rates2.4.1 Discrete Distributions; 2.4.2 Absolutely Continuous Distributions; 2.5 Heavy-Tailed Distributions; 2.5.1 Definition and Basic Properties; 2.5.2 Subexponential Distributions; 2.5.3 Criteria for Subexponentiality and the Class S'; 2.5.4 Pareto Mixtures of Exponentials; 2.6 Detection of Heavy-Tailed Distributions; 2.6.1 Large claims; 2.6.2 Quantile Plots; 2.6.3 Mean Residual Hazard Function; 2.6.4 Extreme Value Statistics; 3 Premiums and Ordering of Risks; 3.1 Premium Calculation Principles; 3.1.1 Desired Properties of "Good" Premiums 3.1.2 Basic Premium Principles3.1.3 Quantile Function: Two More Premium Principles; 3.2 Ordering of Distributions; 3.2.1 Concepts of Utility Theory; 3.2.2 Stochastic Order; 3.2.3 Stop-Loss order; 3.2.4 The Zero Utility Principle; 3.3 Some Aspects of Reinsurance; 4 Distributions of Aggregate Claim Amount; 4.1 Individual and Collective Model; 4.2 Compound Distributions; 4.2.1 Definition and Elementary Properties; 4.2.2 Three Special Cases; 4.2.3 Some Actuarial Applications; 4.2.4 Ordering of Compounds; 4.2.5 The Larger Claims in the PortfoIio; 4.3 Claim Number Distributions 4.3.1 Classical Examples Panjer's Recurrence Relation; 4.3.2 Discrete Compound Poisson Distributions; 4.3.3 Mixed Poisson Distributions; 4.4 Recursive Computation Methods; 4.4.1 The Individual Model: De Pril's Algorithm; 4.4.2 The Collective Model: Panjer's Algorithm; 4.4.3 A Continuous Version of Panjer's Algorithm; 4.5 Lundberg Bounds; 4.5.1 Geometric Compounds; 4.5.2 More General Compound Distributions; 4.5.3 Estimation of the Adjustment Coefficient; 4.6 Approximation by Compound Distributions; 4.6.1 The Total Variation Distance; 4.6.2 The Compound Poisson Approximation 4.6.3 Homogeneous Portfolio |
| Record Nr. | UNINA-9910134839803321 |
| Chicester, : J. Wiley, 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stochastic processes for insurance and finance [[electronic resource] /] / Tomasz Rolski ... [et al.]
| Stochastic processes for insurance and finance [[electronic resource] /] / Tomasz Rolski ... [et al.] |
| Pubbl/distr/stampa | Chicester, : J. Wiley, 1999 |
| Descrizione fisica | 1 online resource (683 p.) |
| Disciplina |
332
368.015192 |
| Altri autori (Persone) | RolskiTomasz |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Insurance - Mathematical models
Finance - Mathematical models Stochastic processes |
| ISBN |
9786612307928
0-470-31788-4 1-282-30792-4 0-470-86042-1 0-470-31704-3 0-585-27223-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Stochastic Processes for Insurance and Finance; Contents; Preface; List of Principal Notation; 1 Concepts from Insurance and Finance; 1.1 Introduction; 1.2 The Claim Number Process; 1.2.1 Renewal Processes; 1.2.2 Mixed Poisson Processes; 1.2.3 Some Other Models; 1.3 The Claim Size Process; 1.3.1 Dangerous Risks; 1.3.2 The Aggregate Claim Amount; 1.3.3 Comparison of Risks; 1.4 Solvability of the Portfolio; 1.4.1 Premiums; 1.4.2 The Risk Reserve; 1.4.3 Economic Environment; 1.5 Reinsurance; 1.5.1 Need for Reinsurance; 1.5.2 Types of Reinsurance; 1.6 Ruin Problems; 1.7 Related Financial Topics
1.7.1 Investment of Surplus1.7.2 Diffusion Processes; 1.7.3 Equity Linked Life Insurance; 2 Probability Distributions; 2.1 Random Variables and Their Characteristics; 2.1.1 Distributions of Random Variables; 2.1.2 Basic Characteristics; 2.1.3 Independence and Conditioning; 2.1.4 Convolution; 2.1.5 Transforms; 2.2 Parametrized Families of Distributions; 2.2.1 Discrete Distributions; 2.2.2 Absolutely Continuous Distributions; 2.2.3 Parametrized Distributions with Heavy Tail; 2.2.4 Operations on Distributions; 2.2.5 Some Special Functions; 2.3 Associated Distributions 2.4 Distributions with Monotone Hazard Rates2.4.1 Discrete Distributions; 2.4.2 Absolutely Continuous Distributions; 2.5 Heavy-Tailed Distributions; 2.5.1 Definition and Basic Properties; 2.5.2 Subexponential Distributions; 2.5.3 Criteria for Subexponentiality and the Class S'; 2.5.4 Pareto Mixtures of Exponentials; 2.6 Detection of Heavy-Tailed Distributions; 2.6.1 Large claims; 2.6.2 Quantile Plots; 2.6.3 Mean Residual Hazard Function; 2.6.4 Extreme Value Statistics; 3 Premiums and Ordering of Risks; 3.1 Premium Calculation Principles; 3.1.1 Desired Properties of "Good" Premiums 3.1.2 Basic Premium Principles3.1.3 Quantile Function: Two More Premium Principles; 3.2 Ordering of Distributions; 3.2.1 Concepts of Utility Theory; 3.2.2 Stochastic Order; 3.2.3 Stop-Loss order; 3.2.4 The Zero Utility Principle; 3.3 Some Aspects of Reinsurance; 4 Distributions of Aggregate Claim Amount; 4.1 Individual and Collective Model; 4.2 Compound Distributions; 4.2.1 Definition and Elementary Properties; 4.2.2 Three Special Cases; 4.2.3 Some Actuarial Applications; 4.2.4 Ordering of Compounds; 4.2.5 The Larger Claims in the PortfoIio; 4.3 Claim Number Distributions 4.3.1 Classical Examples Panjer's Recurrence Relation; 4.3.2 Discrete Compound Poisson Distributions; 4.3.3 Mixed Poisson Distributions; 4.4 Recursive Computation Methods; 4.4.1 The Individual Model: De Pril's Algorithm; 4.4.2 The Collective Model: Panjer's Algorithm; 4.4.3 A Continuous Version of Panjer's Algorithm; 4.5 Lundberg Bounds; 4.5.1 Geometric Compounds; 4.5.2 More General Compound Distributions; 4.5.3 Estimation of the Adjustment Coefficient; 4.6 Approximation by Compound Distributions; 4.6.1 The Total Variation Distance; 4.6.2 The Compound Poisson Approximation 4.6.3 Homogeneous Portfolio |
| Record Nr. | UNINA-9910677849903321 |
| Chicester, : J. Wiley, 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||