Risk modelling in general insurance
להגדלת הטקסט להקטנת הטקסט- ספר
Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short-term risk modelling, model-based pricing, risk-sharing, ruin theory and credibility. It covers much of the international syllabuses for professional actuarial examinations in risk models, but goes into further depth, with worked examples, exercises and detailed case studies. The authors also use the statistical package R to demonstrate how simple code and functions can be used profitably in an actuarial context. The authors' engaging and pragmatic approach, balancing rigour and intuition and developed over many years of teaching the subject, makes this book ideal for self-study or for students taking courses in risk modelling.
כותר |
Risk modelling in general insurance : from principles to practice / Roger J. Gray, Susan M. Pitts. |
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מוציא לאור |
Cambridge New York : Cambridge University Press |
שנה |
2012 |
הערות |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). English |
הערת תוכן ותקציר |
Cover Risk Modelling in General Insurance Series Page Title Copyright Contents Preface 1: Introduction 1.1 The aim of this book 1.2 Notation and prerequisites 1.2.1 Probability 1.2.2 Statistics 1.2.3 Simulation 1.2.4 The statistical software package R 2: Models for claim numbers and claim sizes 2.1 Distributions for claim numbers 2.1.1 Poisson distribution 2.1.2 Negative binomial distribution 2.1.3 Geometric distribution 2.1.4 Binomial distribution 2.1.5 A summary note on R 2.2 Distributions for claim sizes 2.2.1 A further summary note on R 2.2.2 Normal (Gaussian) distribution2.2.3 Exponential distribution 2.2.4 Gamma distribution 2.2.5 Fat-tailed distributions 2.2.6 Lognormal distribution 2.2.7 Pareto distribution 2.2.8 Weibull distribution 2.2.9 Burr distribution 2.2.10 Loggamma distribution 2.3 Mixture distributions 2.4 Fitting models to claim-number and claim-size data 2.4.1 Fitting models to claim numbers 2.4.2 Fitting models to claim sizes Exercises 3: Short term risk models 3.1 The mean and variance of a compound distribution 3.2 The distribution of a random sum 3.2.1 Convolution series formula for a compound distribution3.2.2 Moment generating function of a compound distribution 3.3 Finite mixture distributions 3.4 Special compound distributions 3.4.1 Compound Poisson distributions 3.4.2 Compound mixed Poisson distributions 3.4.3 Compound negative binomial distributions 3.4.4 Compound binomial distributions 3.5 Numerical methods for compound distributions 3.5.1 Panjer recursion algorithm 3.5.2 The fast Fourier transform algorithm 3.6 Approximations for compound distributions 3.6.1 Approximations based on a few moments 3.6.2 Asymptotic approximations3.7 Statistics for compound distributions 3.8 The individual risk model 3.8.1 The mean and variance for the individual risk model 3.8.2 The distribution function and moment generating function for the individual risk model 3.8.3 Approximations for the individual risk model 4: Model based pricing - setting premiums 4.1 Premium calculation principles 4.1.1 The expected value principle (EVP) 4.1.2 The standard deviation principle (SDP) 4.1.3 The variance principle (VP) 4.1.4 The quantile principle (QP) 4.1.5 The zero utility principle (ZUP) 4.1.6 The exponential premium principle (EPP)4.1.7 Some desirable properties of premium calculation principles 4.1.8 Other premium calculation principles 4.2 Maximum and minimum premiums 4.3 Introduction to credibility theory 4.4 Bayesian estimation 4.4.1 The posterior distribution 4.4.2 The wider context of decision theory 4.4.3 The binomial/beta model 4.4.4 The Poisson/gamma model 4.4.5 The normal/normal model 4.5 Bayesian credibility theory 4.5.1 Bayesian credibility estimates under the Poisson/gamma model 4.5.2 Bayesian credibility premiums under the normal/normal model 4.6 Empirical Bayesian credibility theory: Model 1 - the Bühlmann model |
סדרה |
International series on actuarial science |
היקף החומר |
1 online resource (xiv, 393 pages) : digital, PDF file(s). |
שפה |
אנגלית |
מספר מערכת |
997010718725505171 |
תצוגת MARC
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