Stochastic Risk Analysis and Management.
Boris. Harlamov
Bok Engelsk 2017 · Electronic books.
| Omfang | 1 online resource (169 pages)
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| Opplysninger | Cover -- Title Page -- Copyright -- Contents -- 1. Mathematical Bases -- 1.1. Introduction to stochastic risk analysis -- 1.1.1. About the subject -- 1.1.2. About the ruin model -- 1.2. Basic methods -- 1.2.1. Some concepts of probability theory -- 1.2.2. Markov processes -- 1.2.3. Poisson process -- 1.2.4. Gamma process -- 1.2.5. Inverse gamma process -- 1.2.6. Renewal process -- 2. Cramér-Lundberg Model -- 2.1. Infinite horizon -- 2.1.1. Initial probability space -- 2.1.2. Dynamics of a homogeneous insurance company portfolio -- 2.1.3. Ruin time -- 2.1.4. Parameters of the gain process -- 2.1.5. Safety loading -- 2.1.6. Pollaczek-Khinchin formula -- 2.1.7. Sub-probability distribution G+ -- 2.1.8. Consequences from the Pollaczek-Khinchin formula -- 2.1.9. Adjustment coefficient of Lundberg -- 2.1.10. Lundberg inequality -- 2.1.11. Cramér asymptotics -- 2.2. Finite horizon -- 2.2.1. Change of measure -- 2.2.2. Theorem of Gerber -- 2.2.3. Change of measure with parameter gamma -- 2.2.4. Exponential distribution of claim size -- 2.2.5. Normal approximation -- 2.2.6. Diffusion approximation -- 2.2.7. The first exit time for the Wiener process -- 3. Models With the Premium Dependent on the Capital -- 3.1. Definitions and examples -- 3.1.1. General properties -- 3.1.2. Accumulation process -- 3.1.3. Two levels -- 3.1.4. Interest rate -- 3.1.5. Shift on space -- 3.1.6. Discounted process -- 3.1.7. Local factor of Lundberg -- 4. Heavy Tails -- 4.1. Problem of heavy tails -- 4.1.1. Tail of distribution -- 4.1.2. Subexponential distribution -- 4.1.3. Cramér-Lundberg process -- 4.1.4. Examples -- 4.2. Integro-differential equation -- 5. Some Problems of Control -- 5.1. Estimation of probability of ruin on a finite interval -- 5.2. Probability of the credit contract realization -- 5.2.1. Dynamics of the diffusion-type capital.. - 5.3. Choosing the moment at which insurance begins -- 5.3.1. Model of voluntary individual insurance -- 5.3.2. Non-decreasing continuous semi-Markov process -- Bibliography -- Index -- Other titles from iSTE in Mathematics and Statistics -- EULA.
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| ISBN | 9781119388876
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