The American Term Life Insurance History Project – Mathematics of Life Insurance

Mathematics of Life Insurance
L. Wayland Dowling
First Edition, 1925
Cover and front pagePDF
Table of ContentsPDF
Chapter I

  • Compound Interest
  • Present Value
  • Annuities
  • Present Value of a Term Annuity
  • Alternative Proofs
  • Present Value of an Annuity-due
  • General Remark
  • Factorials
  • Independent Events
  • Arrangements or Permutations
  • Combinations or Groups
  • Binomial Coefficients

Chapter II
Theory of Probability

  • Fundamental Principles
  • Bernoulli’s Theorem
  • Compound Probability
  • Total Probability
  • Repeated Trials
  • Expectation in n trials

Chapter III
The Mortality Table

  • Definition
  • The Life Curve
  • Probability of Living or Dying
  • Population
  • Central Death Rate
  • Expectation of Life
  • Probable Lifetime
  • Mathematical Expectation
  • Biometric Functions

Chapter IV
Contingent Functions Endowments and Annuities

  • Pure Endowments
  • Commutation Symbols
  • Contingent Annuities
  • Intercepted Annuities

Chapter V
Contingent Functions
Life Insurance Policies. Net Premiums

  • Whole Life Insurance. Net Single Premium
  • Intercepted Insurance. Net Single Premium
  • Sufficiency Test for Net Single Premium
  • Whole Life Insurance. Net Annual Premium
  • Limited-payment Polices
  • Intercepted Insurance. Net Annual Premium
  • Sufficiency Test for Annual Premium
  • Endowment Insurance
  • Annuities Payable Oftener than Once a Year
  • Premiums Payable Oftener than Once a Year

Chapter VI
Valuation of Policies

  • General Methods for Finding Policy Values
  • Prospective Method
  • Retrospective Method
  • Equivalence of Prospective and Retrospective Methods
  • Accounting or Accumulation Method
  • Fackler Valuation Symbols
  • Cost of Insurance
  • Cost in Terms of Premium
  • Valuation in Terms of Cost
  • Preliminary Term Valuation
  • Modified Preliminary Term Valuation

Chapter VII
Policy Options. Loading. Surplus

  • Options
  • Surrender Value
  • Paid-up Insurance
  • Extension of Insurance
  • Loading
  • Surplus

Chapter VIII
Increasing Insurances

  • Increasing Insurance
  • Intercepted Increase Insurance
  • Return-premium Policies

Chapter IX
Joint Contingent Functions
Part I. Theoretical Development

  • Joint Contingent Functions
  • Joint Endowments
  • Each Person’s Share of the Present Value of a Survivor Endowment
  • Joint Annuities
  • Joint Annuities-due
  • Joint Insurance
  • Instalment Insurances

Joint Contingent Functions
Part II Numerical Computation

  • Joint Endowments
  • Commutation Symbols for Two or More Lives
  • Force of Mortality
  • Equal Age
  • Law of Uniform Seniority
  • A Mahehamized Table of Mortality
  • Probability of Living
  • Commutation Symbols Continued


  • General Remarks
  • Stirling’s Formula
  • Probability of Expectation
  • Deviation
  • Probability of Deviation
  • Probability of Deviation Lying Between Given Limits
  • Probable Deviation
  • Mean Deviation
  • Standard Deviation
  • Recapitulation

  • I. Compound Amount of 1 and Present Value of 1 at 3 1/2%
  • American Experience Table of Mortality
  • Commutation Columns and Valuation Symbols, American Experience Table at 3 1/2%
  • Hunter’s Makehamized American Experience Table. Commutation Columns at 3 1/2%

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