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Actuarial Mathematics (Lecture Notes)

# Actuarial Mathematics (Lecture Notes) - Lecture Notes on...

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Lecture Notes on Actuarial Mathematics Jerry Alan Veeh May 9, 2003 Copyright 2003 Jerry Alan Veeh. All rights reserved.

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§ 0. Introduction The objective of these notes is to present the basic aspects of the theory of insurance, concentrating on the part of this theory related to life insurance. An understanding of the basic principles underlying this part of the subject will form a solid foundation for further study of the theory in a more general setting. Throughout these notes are various exercises and problems. The reader should attempt to work all of these. A calculator, such as the one allowed on the Society of Actuaries examinations, will be useful in solving some of the problems here. The problems contained here are not all amenable to solution using only this simple calculator. A computer equipped with spreadsheet software will sometimes be useful, especially for the laboratory exercises. Copyright 2003 Jerry Alan Veeh. All rights reserved.
§ 1. Overview The central theme of these notes is embodied in the question, “What is the value today of a random sum of money which will be paid at a random time in the future?” Such a random payment is called a contingent payment. The theory of insurance can be viewed as the theory of contingent payments. The insurance company makes payments to its insureds contingent upon the oc- currence of some event, such as the death of the insured, an auto accident by an insured, and so on. The insured makes premium payments to the insurance company contingent upon being alive, having sufficient funds, and so on. A natural way to model these contingencies mathematically is to use probability theory. Probabilistic considerations will, therefore, play an important role in the discussion that follows. The other central consideration in the theory of insurance is the time value of money. Both claims and premium payments occur at various, possibly random, points of time in the future. Since the value of a sum of money depends on the point in time at which the funds are available, a method of comparing the value of sums of money which become available at different points of time is needed. This methodology is provided by the theory of interest. The theory of interest will be studied first in a non-random setting in which all payments are assumed to be sure to be made. Then the theory will be developed in a random environment, and will be seen to provide a complete framework for the understanding of contingent payments. Copyright 2003 Jerry Alan Veeh. All rights reserved.

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§ 2. Elements of the Theory of Interest A typical part of most insurance contracts is that the insured pays the insurer a fixed premium on a periodic (usually annual or semi–annual) basis. Money has time value, that is, \$1 in hand today is more valuable than \$1 to be received one year hence. A careful analysis of insurance problems must take this effect into account.
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Actuarial Mathematics (Lecture Notes) - Lecture Notes on...

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