An Introduction to Actuarial Mathematics
这本书介绍了精算数学的基础，包括金融数学、死亡率函数、人寿保险合同、保费和准备金计算，适合本科生学习人寿保险的基本计算。
An Introduction to Actuarial Mathematics, by A. K. Gupta and T. Varga, 2002, Dordrect: Kluwer Academic Publishers In just a few chapters, the fundamentals of actuarial mathematics are covered in this book by Gupta and Varga. An introduction to financial mathematics comes first; mortality functions, main life insurance contracts, premiums, and reserves calculation are dealt with in the following sections. The volume represents a good example of an institutional textbook about the mathematics of life insurance. The rigorous--but not so terribly high--level of actuarial sophistication adopted by the authors is one, probably the main, of the added values, which can be appreciated by the target readers. As specified in the preface, in practice these are undergraduate students to be provided with the conceptual and statistical tools needed to gain a perspective into the basic calculus of life policies. A much wider audience could be interested in the offered contents, anyway, as suggested by the friendly writing style. The first chapter goes to the very fundamentals of financial mathematics: compound interest, present value, and annuities are the titles of three paragraphs, which constitute the first approach to the subject matter. That is a formal approach, based on a set of key theorems and an abundant series of most useful examples, which also characterize the treatment throughout the book. Problems and questions, as complementary exercise tools, may be found at the end of each paragraph; and this is the standard for the subsequent sections as well. Mortality is the topic addressed in the second chapter, which represents some sort of bridge between the institutional notions given at the beginning and the contracts. Basic theory of mortality, mortality functions, and an easy readable guide to the mortality tables are presented here. Before dealing with individual policies and their specific features, the authors also give the reader some hints on the theory of life insurance, described as a combination of financial mathematics and mortality theory. The great significance for insurance companies of the concept of stochastic cash flow is deeply explained in the first paragraph of the third chapter: Amounts related to both contingent payments by insured persons and payments by the company on death or survival are recognised, properly, as stochastic, and the calculation of expected present values is illustrated. …