From the reviews: "The highly esteemed 1990 first edition of this book now appears in a much expanded second edition. The difference between the first two English editions is entirely due to the addition of numerous exercises. The result is a truly excellent book, balancing ideally between theory and practice. ....As already hinted at above, this book provides the ideal bridge between the classical (deterministic) life insurance theory and the emerging dynamic models based on stochastic processes and the modern theory of finance. The structure of the bridge is very solid, though at the same time pleasant to walk along. I have no doubt that Gerber's book will become the standard text for many years to come.
Metrika, 44, 1996, 2|A modern introduction to the theory of life contingencies, using the probabilistic model. A survey of the mathematics of compound interest is given, and the numerical evaluation of the distribution of aggregate claims, statistical problem of estimating death rates and other probabilities of decrement are discussed. The book contains numerous exercises (with solutions). Already in its 3rd edition.
1 The Mathematics of Compound Interest.- 2 The Future Lifetime of a Life Aged x.- 3 Life Insurance.- 4 Life Annuities.- 5 Net Premiums.- 6 Net Premium Reserves.- 7 Multiple Decrements.- 8 Multiple Life Insurance.- 9 The Total Claim Amount in a Portfolio.- 10 Expense Loadings.- 11 Estimating Probabilities of Death.- Appendix A. Commutation Functions.- A.1 Introduction.- A.2 The Deterministic Model.- A.3 Life Annuities.- A.4 Life Insurance.- A.5 Net Annual Premiums and Premium Reserves.- Appendix B. Simple Interest.- Appendix C. Exercises.- C.0 Introduction.- C.1 Mathematics of Compound Interest: Exercises.- C.1.1 Theory Exercises.- C.1.2 Spreadsheet Exercises.- C.2.1 Theory Exercises.- C.2.2 Spreadsheet Exercises.- C.3 Life Insurance.- C.3.1 Theory Exercises.- C.3.2 Spreadsheet Exercises.- C.4 Life Annuities.- C.4.1 Theory Exercises.- C.4.2 Spreadsheet Exercises.- C.5 Net Premiums.- C.5.1 Notes.- C.5.2 Theory Exercises.- C.5.3 Spreadsheet Exercises.- C.6 Net Premium Reserves.- C.6.1 Theory Exercises.- C.6.2 Spreadsheet Exercises.- C.7 Multiple Decrements: Exercises.- C.7.1 Theory Exercises.- C.8 Multiple Life Insurance: Exercises.- C.8.1 Theory Exercises.- C.8.2 Spreadsheet Exercises.- C.9 The Total Claim Amount in a Portfolio.- C 9.1 Theory Exercises.- C.10 Expense Loadings.- C.10.1 Theory Exercises.- C.10.2 Spreadsheet Exercises.- C.11 Estimating Probabilities of Death.- C.11.1 Theory Exercises.- Appendix D. Solutions.- D.0 Introduction.- D.1 Mathematics of Compound Interest.- D.1.1 Solutions to Theory Exercises.- D.1.2 Solutions to Spreadsheet Exercises.- D.2.1 Solutions to Theory Exercise.- D.2.2 Solutions to Spreadsheet Exercises.- D.3 Life Insurance.- D.3.1 Solutions to Theory Exercises.- D.3.2 Solution to Spreadsheet Exercises.- D.4 Life Annuities.- D.4.1 Solutions to Theory Exercises.- D.4.2 Solutions to Spreadsheet Exercises.- D.5 Net Premiums: Solutions.- D.5.1 Theory Exercises.- D.5.2 Solutions to Spreadsheet Exercises.- D.6 Net Premium Reserves: Solutions.- D.6.1 Theory Exercises.- D.6.2 Solutions to Spreadsheet Exercises.- D.7 Multiple Decrements: Solutions.- D.7.1 Theory Exercises.- D.8 Multiple Life Insurance: Solutions.- D 8.1 Theory Exercises.- D.8.2 Solutions to Spreadsheet Exercises.- D.9 The Total Claim Amount in a Portfolio.- D.9.1 Theory Exercises.- D.10 Expense Loadings.- D.10.1 Theory Exercises.- D.10.2 Spreadsheet Exercises.- D.11 Estimating Probabilities of Death.- D.11.1 Theory Exercises.- Appendix E. Tables.- E.0 Illustrative Life Tables.- E.1 Commutation Columns.- E.2 Multiple Decrement Tables.- References.
This concise introduction to life contingencies, the theory behind the actuarial work around life insurance and pension funds, will appeal to the reader who likes applied mathematics. In addition to model of life contingencies, the theory of compound interest is explained and it is shown how mortality and other rates can be estimated from observations. The probabilistic model is used consistently throughout the book. Numerous exercises (with answers and solutions) have been added, and for this third edition several misprints have been corrected.
From the reviews: "The highly esteemed 1990 first edition of this book now appears in a much expanded second edition. ....As already hinted at above, this book provides the ideal bridge between the classical (deterministic) life insurance theory and the emerging dynamic models based on stochastic processes and the modern theory of finance.
Das Buch bietet dem mathematisch orientierten Leser eine moderne Einführung in die Lebensversicherungsmathematik, bei der das Modell der Wahrscheinlichkeitsrechnung konsequent verwendet wird. Daneben wird auch ein Überblick über die Zinsrechnung gegeben, und die numerische Berechnung der Verteilung des Totalschadens sowie das statistische Problem der Schätzung von Ausscheidewahrscheinlichkeiten werden diskutiert.
From the reviews: "The highly esteemed 1990 first edition of this book now appears in a much expanded second edition. The difference between the first two English editions is entirely due to the addition of numerous exercises. The result is a truly excellent book, balancing ideally between theory and practice. ....As already hinted at above, this book provides the ideal bridge between the classical (deterministic) life insurance theory and the emerging dynamic models based on stochastic processes and the modern theory of finance. The structure of the bridge is very solid, though at the same time pleasant to walk along. I have no doubt that Gerber's book will become the standard text for many years to come.
Metrika, 44, 1996, 2
Inhaltsverzeichnis
1 The Mathematics of Compound Interest.- 2 The Future Lifetime of a Life Aged x.- 3 Life Insurance.- 4 Life Annuities.- 5 Net Premiums.- 6 Net Premium Reserves.- 7 Multiple Decrements.- 8 Multiple Life Insurance.- 9 The Total Claim Amount in a Portfolio.- 10 Expense Loadings.- 11 Estimating Probabilities of Death.- Appendix A. Commutation Functions.- A.1 Introduction.- A.2 The Deterministic Model.- A.3 Life Annuities.- A.4 Life Insurance.- A.5 Net Annual Premiums and Premium Reserves.- Appendix B. Simple Interest.- Appendix C. Exercises.- C.0 Introduction.- C.1 Mathematics of Compound Interest: Exercises.- C.1.1 Theory Exercises.- C.1.2 Spreadsheet Exercises.- C.2.1 Theory Exercises.- C.2.2 Spreadsheet Exercises.- C.3 Life Insurance.- C.3.1 Theory Exercises.- C.3.2 Spreadsheet Exercises.- C.4 Life Annuities.- C.4.1 Theory Exercises.- C.4.2 Spreadsheet Exercises.- C.5 Net Premiums.- C.5.1 Notes.- C.5.2 Theory Exercises.- C.5.3 Spreadsheet Exercises.- C.6 Net Premium Reserves.- C.6.1 Theory Exercises.- C.6.2 Spreadsheet Exercises.- C.7 Multiple Decrements: Exercises.- C.7.1 Theory Exercises.- C.8 Multiple Life Insurance: Exercises.- C.8.1 Theory Exercises.- C.8.2 Spreadsheet Exercises.- C.9 The Total Claim Amount in a Portfolio.- C 9.1 Theory Exercises.- C.10 Expense Loadings.- C.10.1 Theory Exercises.- C.10.2 Spreadsheet Exercises.- C.11 Estimating Probabilities of Death.- C.11.1 Theory Exercises.- Appendix D. Solutions.- D.0 Introduction.- D.1 Mathematics of Compound Interest.- D.1.1 Solutions to Theory Exercises.- D.1.2 Solutions to Spreadsheet Exercises.- D.2.1 Solutions to Theory Exercise.- D.2.2 Solutions to Spreadsheet Exercises.- D.3 Life Insurance.- D.3.1 Solutions to Theory Exercises.- D.3.2 Solution to Spreadsheet Exercises.- D.4 Life Annuities.- D.4.1 Solutions to Theory Exercises.- D.4.2 Solutions to Spreadsheet Exercises.- D.5 Net Premiums: Solutions.- D.5.1 Theory Exercises.- D.5.2 Solutions to Spreadsheet Exercises.- D.6 Net Premium Reserves: Solutions.- D.6.1 Theory Exercises.- D.6.2 Solutions to Spreadsheet Exercises.- D.7 Multiple Decrements: Solutions.- D.7.1 Theory Exercises.- D.8 Multiple Life Insurance: Solutions.- D 8.1 Theory Exercises.- D.8.2 Solutions to Spreadsheet Exercises.- D.9 The Total Claim Amount in a Portfolio.- D.9.1 Theory Exercises.- D.10 Expense Loadings.- D.10.1 Theory Exercises.- D.10.2 Spreadsheet Exercises.- D.11 Estimating Probabilities of Death.- D.11.1 Theory Exercises.- Appendix E. Tables.- E.0 Illustrative Life Tables.- E.1 Commutation Columns.- E.2 Multiple Decrement Tables.- References.
A modern introduction to the theory of life contingencies, using the probabilistic model. A survey of the mathematics of compound interest is given, and the numerical evaluation of the distribution of aggregate claims, statistical problem of estimating death rates and other probabilities of decrement are discussed. The book contains numerous exercises (with solutions). Already in its 3rd edition.
