Premium Calculation Principles and their Properties

Book is devoted to the analysis of the most widely used methods of pricing of insurance contracts with known distributions of the future losses and their properties. All properties formulated in the book are presented together with their proofs. Several characterization theorems formulated in a form of necessary and sufficient conditions for certain properties to be hold are presented. Monotonicity and limit behavior of insurance premiums dependent on parameters are also studied. Book contains a large number of examples of premium calculations for different claim distributions taking into account random appearance of the claim and random size of the claim. We demonstrate also concepts of ogramming of described mathematical algorithms in MatLab GUI and present tables of numerical illustrations for different model parameters. Book was written on the level accessible for students finishing actuarial and financial master educational programs and can be interesting to read and to use for actuaries and computer programmers working in the insurance industry as well as for other readers willing to know haw prices for insurance contracts are calculated.