Summary |
The book is intended for a broad audience. The theory is developed from the perspective of application to real insurance data.
Chapters 1-4 provide the basic mathematical and statistical tools that are used in the remaining chapters. Chapter 1 develops the Laplace transform which is the basic mathematical tool used throughout the book to develop the theory. Chapter 2 provides the basic probabilistic background necessary for the book. Chapter 3 which deals with basic stochastic processes. Chapter 4 provides the plethora of continuous and discrete distributions used in the subsequent chapters. Chapter 5 deals with what has been traditionally called the “individual risk” model with its background in life insurance. The computational results presented were all developed in the 1980’s and are related to those in chapter 6. Chapters 6-9 deal with the “collective” risk with us background in primarily non-life branches of insurance such as health, property, casualty, liability and catastrophe insurance. Chapter 6 focuses on the Poisson, negative binomial, binomial and related distributions for claim counts. Generalizations of these models through the mechanism of compounding are given in chapter 7. Similar generalizations using mixing or “parameter uncertainty” are the subject of chapter 8. In chapter 9, the problems of selection, fitting and validation of the distributions is addressed. Chapter 10 is different in the sense that simple analytic formulas for the extreme right hand tail of the distribution of aggregate claims are developed. This provides insight into the effect of the selection of any of the claim count of size-of-loss distributions and useful approximations when computations become prohibitive or when a quick estimate is required. Chapter 11 is devoted to traditional ruin theory. The emphasis is on approximate and exact calculation of ruin probabilities used the mathematical tools in previous chapters.
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