Fundamentals of Actuarial Mathematics [Hardcover]

• 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 several spreadsheet examples throughout.

• Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies

• Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the Black-Scholes formula will be introduced.

Preface xvii

Acknowledgements xxi

Notation index xxiii

Part I THE DETERMINISTIC LIFE CONTINGENCIES MODEL 1

1 Introduction and motivation 3

1.1 Risk and insurance 3

1.2 Deterministic versus stochastic models 4

1.3 Finance and investments 5

1.4 Adequacy and equity 5

1.5 Reassessment 6

1.6 Conclusion 6

2 The basic deterministic model 7

2.1 Cash flows 7

2.2 An analogy with currencies 8

2.3 Discount functions 9

2.4 Calculating the discount function 11

2.5 Interest and discount rates 12

2.6 Constant interest 12

2.7 Values and actuarial equivalence 13

2.8 Vector notation 17

2.9 Regular pattern cash flows 18

2.10 Balances and reserves 20

2.11 Time shifting and the splitting identity 26

2.11 Change of discount funclӠ