Risk Measures and Insurance Solvency Benchmarks
portes grátis
Risk Measures and Insurance Solvency Benchmarks
Fixed-Probability Levels in Renewal Risk Models
Malinovskii, Vsevolod K.
Taylor & Francis Ltd
07/2023
340
Mole
Inglês
9780367744021
15 a 20 dias
Descrição não disponível.
1. Risk measures in finance and insurance. 1.1. Risk measures in finance and portfolio management. 1.2. Risk measures in Solvency II system. 1.3. Risk measures in risk theory. 1.4. Aim and structure of the book. 1.5. Readers, to whom this book is addressed. Problems. 2. Fixed-probability level in a diffusion model. 2.1. Diffusion model: an auxiliary tool. 2.2. Direct level-crossing problem. 2.3. Inverse level-crossing problem. 2.4. Asymptotic behaviour of fixed-probability level. 2.5. Primary upper bounds on fixed-probability level. 2.6. Elaborated upper bounds on fixed-probability level. 2.7. Conclusions and perspectives. Problems. 3. Fixed-probability level in an exceptional renewal model. 3.1. Exponential renewal model: an exceptional case. 3.2. Direct level-crossing problem. 3.3. Inverse level-crossing problem. 3.4. Asymptotic behaviour of fixed-probability level. 3.5. Primary upper bounds on fixed-probability level. 3.6. Elaborated upper bounds on fixed-probability level. 3.7. Conclusions. Problems. 4. Implicit function defined by M-equation. 4.1. Analytical properties of core integral expression. 4.2. Proximity between Mu;c(t) and Mu;c(t j v). 4.3. Analytical properties of M-level. Problem. 5. Fixed-probability level in general renewal model. 5.1. General renewal model: main framework. 5.2. Direct level-crossing problem. 5.3. Inverse level-crossing problem. 5.4. Primary upper bounds on fixed-probability level. 5.5. Proximity to M-level. 5.6. Conclusion. Problem. 6. Case study: numerical evaluation of fixed-probability Level. 6.1. Distributions of T and Y selected for numerical calculations. 6.2. Simulation in level-crossing problems. 6.3. Numerically calculated bounds on the fixed-probability level. 6.4. Conclusion. Problems. 7. Probability mechanism of insurance with migration and ERS-analysis. 7.1. Structural model of insurance business: origin and purpose of ERS-analysis. 7.2. Price competition, migration, and market price. 7.3. Compound Poisson risk model with migration. 7.4. ERS-analysis, when Y is exponentially distributed. 7.5. ERS-analysis, when Y is generally distributed. 7.6. Conclusions. Problems. A. Auxiliary results from analysis. B. Auxiliary results from probability. List of Notations. Notes and Comments. Bibliography. Index.
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insurance mathematics;stochastic processes;actuarial science;probability theory;asymptotic analysis;financial risk assessment;advanced insurance risk modeling
1. Risk measures in finance and insurance. 1.1. Risk measures in finance and portfolio management. 1.2. Risk measures in Solvency II system. 1.3. Risk measures in risk theory. 1.4. Aim and structure of the book. 1.5. Readers, to whom this book is addressed. Problems. 2. Fixed-probability level in a diffusion model. 2.1. Diffusion model: an auxiliary tool. 2.2. Direct level-crossing problem. 2.3. Inverse level-crossing problem. 2.4. Asymptotic behaviour of fixed-probability level. 2.5. Primary upper bounds on fixed-probability level. 2.6. Elaborated upper bounds on fixed-probability level. 2.7. Conclusions and perspectives. Problems. 3. Fixed-probability level in an exceptional renewal model. 3.1. Exponential renewal model: an exceptional case. 3.2. Direct level-crossing problem. 3.3. Inverse level-crossing problem. 3.4. Asymptotic behaviour of fixed-probability level. 3.5. Primary upper bounds on fixed-probability level. 3.6. Elaborated upper bounds on fixed-probability level. 3.7. Conclusions. Problems. 4. Implicit function defined by M-equation. 4.1. Analytical properties of core integral expression. 4.2. Proximity between Mu;c(t) and Mu;c(t j v). 4.3. Analytical properties of M-level. Problem. 5. Fixed-probability level in general renewal model. 5.1. General renewal model: main framework. 5.2. Direct level-crossing problem. 5.3. Inverse level-crossing problem. 5.4. Primary upper bounds on fixed-probability level. 5.5. Proximity to M-level. 5.6. Conclusion. Problem. 6. Case study: numerical evaluation of fixed-probability Level. 6.1. Distributions of T and Y selected for numerical calculations. 6.2. Simulation in level-crossing problems. 6.3. Numerically calculated bounds on the fixed-probability level. 6.4. Conclusion. Problems. 7. Probability mechanism of insurance with migration and ERS-analysis. 7.1. Structural model of insurance business: origin and purpose of ERS-analysis. 7.2. Price competition, migration, and market price. 7.3. Compound Poisson risk model with migration. 7.4. ERS-analysis, when Y is exponentially distributed. 7.5. ERS-analysis, when Y is generally distributed. 7.6. Conclusions. Problems. A. Auxiliary results from analysis. B. Auxiliary results from probability. List of Notations. Notes and Comments. Bibliography. Index.
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