Fundamentals of actuarial mathematics
Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models, and an introduction to modern mathematical finance.New edition restructures the material to fit into modern computational methods and provides...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
West Sussex, England :
John Wiley & Sons Ltd
2015.
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| Edición: | Third edition |
| Colección: | New York Academy of Sciences Ser.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849114106719 |
Tabla de Contenidos:
- Fundamentals of Actuarial Mathematics; Contents; Preface; Acknowledgements; About the companion website; Part I THE DETERMINISTIC LIFE CONTINGENCIES MODEL; 1 Introduction and motivation; 1.1 Risk and insurance; 1.2 Deterministic versus stochastic models; 1.3 Finance and investments; 1.4 Adequacy and equity; 1.5 Reassessment; 1.6 Conclusion; 2 The basic deterministic model; 2.1 Cash flows; 2.2 An analogy with currencies; 2.3 Discount functions; 2.4 Calculating the discount function; 2.5 Interest and discount rates; 2.6 Constant interest; 2.7 Values and actuarial equivalence
- 2.8 Vector notation2.9 Regular pattern cash flows; 2.10 Balances and reserves; 2.10.1 Basic concepts; 2.10.2 Relation between balances and reserves; 2.10.3 Prospective versus retrospective methods; 2.10.4 Recursion formulas; 2.11 Time shifting and the splitting identity; *2.11 Change of discount function; 2.12 Internal rates of return; *2.13 Forward prices and term structure; 2.14 Standard notation and terminology; 2.14.1 Standard notation for cash flows discounted with interest; 2.14.2 New notation; 2.15 Spreadsheet calculations; Notes and references; Exercises; 3 The life table
- 3.1 Basic definitions3.2 Probabilities; 3.3 Constructing the life table from the values of qx; 3.4 Life expectancy; 3.5 Choice of life tables; 3.6 Standard notation and terminology; 3.7 A sample table; Notes and references; Exercises; 4 Life annuities; 4.1 Introduction; 4.2 Calculating annuity premiums; 4.3 The interest and survivorship discount function; 4.3.1 The basic definition; 4.3.2 Relations between yx for various values of x; 4.4 Guaranteed payments; 4.5 Deferred annuities with annual premiums; 4.6 Some practical considerations; 4.6.1 Gross premiums; 4.6.2 Gender aspects
- 4.7 Standard notation and terminology4.8 Spreadsheet calculations; Exercises; 5 Life insurance; 5.1 Introduction; 5.2 Calculating life insurance premiums; 5.3 Types of life insurance; 5.4 Combined insurance-annuity benefits; 5.5 Insurances viewed as annuities; 5.6 Summary of formulas; 5.7 A general insurance-annuity identity; 5.7.1 The general identity; 5.7.2 The endowment identity; 5.8 Standard notation and terminology; 5.8.1 Single-premium notation; 5.8.2 Annual-premium notation; 5.8.3 Identities; 5.9 Spreadsheet applications; Exercises; 6 Insurance and annuity reserves
- 6.1 Introduction to reserves6.2 The general pattern of reserves; 6.3 Recursion; 6.4 Detailed analysis of an insurance or annuity contract; 6.4.1 Gains and losses; 6.4.2 The risk-savings decomposition; 6.5 Bases for reserves; 6.6 Nonforfeiture values; 6.7 Policies involving a return of the reserve; 6.8 Premium difference and paid-up formulas; 6.8.1 Premium difference formulas; 6.8.2 Paid-up formulas; 6.8.3 Level endowment reserves; 6.9 Standard notation and terminology; 6.10 Spreadsheet applications; Exercises; 7 Fractional durations; 7.1 Introduction
- 7.2 Cash flows discounted with interest only
