An Introduction to the Mathematics of Finance: A by Stephen Garrett

By Stephen Garrett

An creation to the maths of Finance: A Deterministic process, 2e, bargains a hugely illustrated advent to mathematical finance, with a different emphasis on rates of interest. This revision of the McCutcheon-Scott vintage follows the center topics coated by way of the 1st specialist examination required of united kingdom actuaries, the CT1 examination. It realigns the desk of contents with the CT1 examination and contains pattern questions from prior tests of either The Actuarial career and the CFA Institute. With a wealth of solved difficulties and engaging purposes, An advent to the maths of Finance stands on my own in its skill to deal with the wishes of its basic audience, the actuarial student.

Closely follows the syllabus for the CT1 examination of The Institute and school of Actuaries
Features new content material and extra examples
Includes earlier examination questions from The Institute and school of Actuaries and the CFA Institute

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6 VARYING ANNUITIES Until now we have considered annuities for which the amount of each payment is constant. For an annuity in which the payments are not all of an equal amount, it is a simple matter to find the present (or accumulated) value from first principles. For example, the present value of such an annuity may always be evaluated as n X Xi vti i¼1 where the ith payment, of amount Xi, is made at time ti. 2) The last equation need not be memorized, as it may be rapidly derived from first principles.

00004-7 Ó 2013 Institute and Faculty of Actuaries (RC000243). Published by Elsevier Ltd.

With this notation, an equation such as Xs10 0:04 ¼ 100a15 0:03 is quite precise. This notation is readily extended to the functions defined in later chapters. 7 UNCERTAIN PAYMENTS It is clear that the concept of the equation of value is very important in practice; indeed, it forms the foundation of much of this book. At this stage it is worth emphasizing that the payments (either discrete or continuous) need not be certain for the equation of value to be formed and used. A detailed study of the allowance of uncertain cash flows is beyond the scope of this book, and much of this book involves certain cash flows.

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