This monograph gives a modern overview of insurance mathematics with emphasis on stochastic modelling and the related mathematical methods. The topics are presented in the following main parts.
The first part deals with models for individual and aggregate losses in a portfolio of risks. Individual losses are represented by probability distributions on the positive real axis, which can light and heavy-tailed. The distribution of the maximum of a sample of individual losses has also an important role for the actuarial risk management and asymptotic approximations are presented. Models for compound losses are then presented. These are random sums, compound processes and shot-noise processes.
The second main part of the monograph presents methods for determining the premium rates. The focus is on the credibility theory, which is based on Bayesian statistics. Experience rated premiums and in particular the credibility premium are presented. The Bühlmann Straub model and other general models are shown.
The third part is the actuarial risk or ruin theory. Various stochastic models for the insurer financial surplus, called risk processes, are presented. The main focus is the computation of the probability of ruin, that is, of the probability that the risk process ever falls below the null level. Asymptotic approximations to this probability are presented. The simplest risk process, which is compound Poisson process, is then generalized in various ways: by renewal processes, by various Lévy processes, by compound Poisson processes with inhomogeneous and periodic mean claim occurence and, finally, by considering multidimensional extensions.
The fourth part introduces particular models of life insurance.
The last main part of this monograph introduces important computational techniques. We can distinguish the methods arising from asymptotic analysis, which are the Laplace approximation and the saddlepoint approximation, from Monte Carlo methods, essentially importance sampling. These methods share exponential tilt as common feature.
- This book presents methods for determining the premium rates
- Asymptotic approximations to this probability are presented
- Introduces particular models of life insurance
- Introduces important computational techniques
Scientists, researchers and engineers interested in this subject area
2. Individual losses
3. Compound losses
4. Credibility theory
5. Compound Poisson Risk processes
6. General risk processes
7. Models of life insurance
8. Approximation and computational methods
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- © ISTE Press - Elsevier 2018
- ISTE Press - Elsevier
- Hardcover ISBN:
Ricardo Gatto is an Associate Professor of Statistics, Applied Probability and Actuarial Mathematics at the Institute of Mathematical Statistics and Actuarial Science of the University of Bern
University of Bern, Switzerland