Life Insurance Theory: Actuarial Perspectives

Front Cover
Springer Science & Business Media, Aug 31, 1997 - Business & Economics - 184 pages
This book is different from all other books on Life Insurance by at least one of the following characteristics 1-4. 1. The treatment of life insurances at three different levels: time-capital, present value and price level. We call time-capital any distribution of a capital over time: (*) is the time-capital with amounts Cl, ~, ... , C at moments Tl, T , ..• , T resp. N 2 N For instance, let (x) be a life at instant 0 with future lifetime X. Then the whole oO oO life insurance A is the time-capital (I,X). The whole life annuity is the x x time-capital (1,0) + (1,1) + (1,2) + ... + (I,'X), where 'X is the integer part ofX. The present value at 0 of time-capital (*) is the random variable T1 T TN Cl V + ~ v , + ... + CNV . (**) In particular, the present value ofA 00 and 00 is x x 0 0 2 A = ~ and = 1 + v + v + ... + v'X resp. x x The price (or premium) of a time-capital is the expectation of its present value. In particular, the price ofA 00 and x 00 is x 2 A = E(~) and = E(I + v + v + ... + v'X) resp.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Financial Models
1
13 Variable interest rates
4
14 Deterministic timecapitals
7
15 Stochastic timecapitals
8
16 Annuitiescertain
9
17 Stochastic interests
10
Mortality Models
11
23 Force of mortality
12
Ruin Probability of a Life Insurance Company
83
102 Profit of a contract
84
104 Probability of ruin in a closed portfolio
85
105 Solvency parameter of a portfolio
86
108 Probability of ruin in an open portfolio
87
1010 Open portfolio with exponential growth
88
1012 Evaluation of variances General methodology
89
1013 Deferred life capital
90

24 Decease in the middle of the year
13
25 Expected future lifetime
14
26 Analytic life tables
15
27 Restricted life tables
16
29 Commutation functions
17
Construction of Life Tables
19
32 National tables
20
33 Private tables
21
34 Analytic leastsquares graduation
22
36 Determination of initial parameters in the Makeham case
24
Basic Concepts of Life Insurance Mathematics
25
42 Contracts
26
44 Validity level of relations
27
46 Null events
28
Life Annuities One Life
29
52 Constant life annuities
30
53 Partitioned life annuities
33
54 General variable life annuities
35
55 Classical variable life annuities
37
56 Annuities on status x
40
57 Variable interest rates
41
Life Insurances One Life
43
62 General variable life insurances
46
63 Classical variable life insurances
47
64 Endowments
48
65 Insurance of a remaining debt at death
49
66 Variable interest rates
50
Relations Between Life Annuities and Life Insurances One Life
51
72 Constant annuities and insurances Present value level
52
73 Variable annuities and insurances General discrete case
53
74 Variable annuities and insurances General continuous case
54
75 Classical variable annuities and insurances
55
Decomposition of TimeCapitols One Life
57
82 The decomposition formula
59
83 Evaluation of a reserve at a noninteger instant
60
84 Fourets Formula
62
86 Insurances payable in the middle of the year of death
64
Life Insurance Contracts One Life
65
92 Reserves of a contract
66
93 Practical constraints on contracts
68
94 Contracts with partitioned premiums
69
general endowment insurance
71
97 Positive reserves analytic proofs
72
98 Variation of prices with interest rate i
74
99 Variation of reserves with interest rate i
75
910 Variation of reserves with time t
78
912 Expense loadings
80
1014 General life insurance
91
1016 Variance of reserves
94
Insurance on a Status Several Lives
95
112 Probabilities on a status
97
113 Deferred capitals on a status
100
114 Life annuities on a status
101
115 Life insurances on a status
102
116 Alternative notations
103
Decomposition of TimeCapitals Several Lives
105
122 Timecapitals vanishing at first decease
106
123 The decomposition formula
107
125 Evaluation of a reserve at a noninteger instant
108
126 Fourets formula
109
Life Insurance Contracts Several Lives
111
133 Practical constraints on contracts
112
134 Contracts with partitioned premiums
113
Multiple Decrement Models
115
142 Other graphs
118
143 Events and probabilities on a graph
119
144 Annuities on states of a graph
123
145 Transition capitals on a graph
125
146 Transition Theorem for timecapitals Price level
126
147 Illustration in the case of graph Grxy
128
Variances Several Lives
133
152 Evaluation of variances General methodology
134
153 Deferred life capitals
136
156 Variance of reserves
138
Population groups on a Graph
139
162 Open graph model
140
163 Estimation of instantaneous transition rates
141
164 Estimations in a graph with two states
142
165 Estimations in a graph with three states
145
166 Estimations in a graph with four states
148
167 Evaluation of state probabilities
152
168 State probabilities in a graph with two states
153
1610 State probabilities in a graph with four states
154
1611 Mortality estimations
155
SUMMATION BY PARTS
157
LINEAR INTERPOLATIONS
159
PROBABILITY THEORY
163
A DIFFERENTIAL EQUATION
169
INVERSION OF A POWER SERIES
171
SUMMARY OF FORMULAS
173
References
175
Notation Index
177
Subject Index
181
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information