Preface |
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ix | |
1 Statistical Concepts |
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1 | (40) |
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1 | (6) |
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7 | (7) |
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1.2.1 Discrete Random Variables |
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8 | (2) |
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1.2.2 Continuous Random Variables |
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10 | (3) |
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1.2.3 Mixed Random Variables |
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13 | (1) |
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14 | (6) |
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1.4 Moment Generating Function |
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20 | (2) |
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22 | (3) |
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1.6 Nonnegative Random Variables |
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25 | (4) |
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1.6.1 Pareto Distribution |
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25 | (1) |
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1.6.2 Lognormal Distribution |
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26 | (1) |
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1.6.3 Weibull Distribution |
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26 | (1) |
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1.6.4 Gompertz Distribution |
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27 | (1) |
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1.6.5 Makeham Distribution |
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28 | (1) |
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1.7 Conditional Distributions |
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29 | (2) |
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31 | (5) |
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36 | (2) |
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38 | (1) |
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38 | (3) |
2 Statistical Techniques |
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41 | (52) |
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2.1 Sampling Distributions and Estimation |
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41 | (8) |
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42 | (2) |
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2.1.2 Confidence Intervals |
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44 | (1) |
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2.1.3 Percentiles and Prediction Intervals |
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45 | (1) |
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2.1.4 Confidence and Prediction Sets |
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46 | (3) |
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2.2 Sums of Independent Variables |
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49 | (5) |
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2.3 Order Statistics and Empirical Prediction Intervals |
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54 | (3) |
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2.4 Approximating Aggregate Distributions |
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57 | (8) |
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2.4.1 Central Limit Theorem |
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57 | (4) |
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2.4.2 Haldane Type A Approximation |
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61 | (1) |
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2.4.3 Saddlepoint Approximation |
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62 | (3) |
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2.5 Compound Aggregate Variables |
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65 | (5) |
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2.5.1 Expectations of Compound Aggregate Variables |
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65 | (1) |
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2.5.2 Limiting Distributions for Compound Aggregate Variables |
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66 | (4) |
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70 | (5) |
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2.6.1 Least Squares Estimation |
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71 | (3) |
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2.6.2 Regression Model-Based Inference |
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74 | (1) |
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2.7 Autoregressive Systems |
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75 | (3) |
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78 | (9) |
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2.8.1 Probability Plotting |
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79 | (4) |
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2.8.2 Generalized Least Squares Diagnostic |
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83 | (1) |
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2.8.3 Interval Data Diagnostic |
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84 | (3) |
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87 | (1) |
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88 | (2) |
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90 | (3) |
3 Financial Computational Models |
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93 | (30) |
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3.1 Fixed Financial Rate Models |
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94 | (7) |
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3.1.1 Financial Rate-Based Calculations |
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94 | (5) |
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3.1.2 General Period Discrete Rate Models |
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99 | (1) |
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3.1.3 Continuous-Rate Models |
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100 | (1) |
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101 | (5) |
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3.2.1 Discrete Annuity Models |
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101 | (3) |
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3.2.2 Continuous Annuity Models |
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104 | (2) |
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3.3 Stochastic Rate Models |
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106 | (11) |
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3.3.1 Discrete Stochastic Rate Model |
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106 | (6) |
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3.3.2 Continuous Stochastic Rate Models |
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112 | (2) |
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3.3.3 Discrete Stochastic Annuity Models |
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114 | (2) |
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3.3.4 Continuous Stochastic Annuity Models |
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116 | (1) |
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117 | (2) |
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119 | (1) |
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120 | (3) |
4 Deterministic Status Models |
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123 | (40) |
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123 | (5) |
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4.1.1 Deterministic Loss Models |
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124 | (2) |
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4.1.2 Stochastic Rate Models |
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126 | (2) |
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4.2 Stochastic Loss Criterion |
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128 | (3) |
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129 | (1) |
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4.2.2 Percentile Criteria |
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130 | (1) |
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131 | (9) |
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131 | (4) |
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135 | (1) |
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136 | (3) |
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4.3.4 Option Pricing Diagnostics |
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139 | (1) |
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4.4 Collective Aggregate Models |
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140 | (8) |
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4.4.1 Fixed Number of Variables |
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141 | (2) |
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4.4.2 Stochastic Number of Variables |
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143 | (2) |
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4.4.3 Aggregate Stop-Loss Reinsurance and Dividends |
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145 | (3) |
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4.5 Stochastic Surplus Model |
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148 | (7) |
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4.5.1 Discrete Surplus Model |
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148 | (4) |
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4.5.2 Continuous Surplus Model |
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152 | (3) |
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155 | (3) |
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158 | (1) |
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159 | (4) |
5 Future Lifetime Random Variables and Life Tables |
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163 | (40) |
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5.1 Continuous Future Lifetime |
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164 | (3) |
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5.2 Discrete Future Lifetime |
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167 | (2) |
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169 | (6) |
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175 | (2) |
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5.5 Select Future Lifetimes |
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177 | (2) |
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179 | (3) |
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5.7 Life Models and Life Tables |
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182 | (3) |
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5.8 Life Table Confidence Sets and Prediction Intervals |
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185 | (2) |
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5.9 Life Models and Life Table Parameters |
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187 | (7) |
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5.9.1 Population Parameters |
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188 | (3) |
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5.9.2 Aggregate Parameters |
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191 | (2) |
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5.9.3 Fractional Age Adjustments |
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193 | (1) |
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5.10 Select and Ultimate Life Tables |
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194 | (4) |
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198 | (2) |
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200 | (1) |
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200 | (3) |
6 Stochastic Status Models |
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203 | (54) |
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6.1 Stochastic Present Value Functions |
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204 | (1) |
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205 | (3) |
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6.2.1 Continuous-Risk Calculations |
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205 | (1) |
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6.2.2 Discrete Risk Calculations |
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206 | (1) |
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6.2.3 Mixed Risk Calculations |
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207 | (1) |
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6.3 Percentile Evaluations |
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208 | (2) |
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210 | (5) |
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6.4.1 Types of Unit Benefit Life Insurance |
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212 | (3) |
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215 | (8) |
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6.5.1 Types of Unit Payment Life Annuities |
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217 | (3) |
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6.5.2 Apportionable Annuities |
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220 | (3) |
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6.6 Relating Risk Calculations |
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223 | (4) |
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6.6.1 Relations among Insurance Expectations |
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223 | (2) |
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6.6.2 Relations among Insurance and Annuity Expectations |
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225 | (1) |
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6.6.3 Relations among Annuity Expectations |
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226 | (1) |
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6.7 Actuarial Life Tables |
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227 | (3) |
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6.8 Loss Models and Insurance Premiums |
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230 | (7) |
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6.8.1 Unit Benefit Premium Notation |
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232 | (3) |
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6.8.2 Variance of the Loss Function |
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235 | (2) |
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237 | (7) |
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6.9.1 Unit Benefit Reserves Notations |
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240 | (1) |
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6.9.2 Relations among Reserve Calculations |
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241 | (2) |
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6.9.3 Survivorship Group Approach to Reserve Calculations |
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243 | (1) |
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6.10 General Time Period Models |
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244 | (5) |
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6.10.1 General Period Expectation |
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245 | (1) |
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6.10.2 Relations among General Period Expectations |
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246 | (3) |
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6.11 Expense Models and Computations |
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249 | (3) |
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252 | (2) |
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254 | (1) |
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254 | (3) |
7 Advanced Stochastic Status Models |
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257 | (38) |
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7.1 Multiple Future Lifetimes |
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257 | (7) |
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258 | (2) |
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7.1.2 Last Survivor Status |
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260 | (3) |
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7.1.3 General Contingent Status |
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263 | (1) |
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7.2 Multiple-Decrement Models |
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264 | (16) |
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7.2.1 Continuous Multiple Decrements |
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264 | (2) |
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7.2.2 Forces of Decrement |
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266 | (2) |
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7.2.3 Discrete Multiple Decrements |
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268 | (1) |
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7.2.4 Single-Decrement Probabilities |
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269 | (2) |
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7.2.5 Uniformly Distributed Single-Decrement Rates |
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271 | (2) |
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7.2.6 Single-Decrement Probability Bounds |
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273 | (2) |
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7.2.7 Multiple-Decrement Life Tables |
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275 | (3) |
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7.2.8 Single-Decrement Life Tables |
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278 | (1) |
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7.2.9 Multiple-Decrement Computations |
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279 | (1) |
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280 | (10) |
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7.3.1 Multiple-Decrement Benefits |
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281 | (4) |
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7.3.2 Pension Contributions |
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285 | (2) |
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7.3.3 Future Salary-Based Benefits and Contributions |
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287 | (1) |
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7.3.4 Yearly Based Retirement Benefits |
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288 | (2) |
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290 | (1) |
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291 | (1) |
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292 | (3) |
8 Markov Chain Methods |
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295 | (28) |
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8.1 Introduction to Markov Chains |
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296 | (1) |
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8.2 Nonhomogeneous Stochastic Status Chains |
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297 | (10) |
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8.2.1 Single-Decrement Chains |
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298 | (1) |
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299 | (1) |
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8.2.3 Multiple-Decrement Chains |
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300 | (3) |
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8.2.4 Multirisk Strata Chains |
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303 | (4) |
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8.3 Homogeneous Stochastic Status Chains |
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307 | (5) |
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8.3.1 Expected Curtate Future Lifetime |
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309 | (1) |
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310 | (2) |
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312 | (4) |
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8.4.1 Single-Decrement Models |
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313 | (1) |
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8.4.2 Multiple-Decrement Models |
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314 | (1) |
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8.4.3 Multirisk Strata Models |
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315 | (1) |
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316 | (1) |
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317 | (3) |
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320 | (3) |
9 Scenario and Simulation Testing |
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323 | (30) |
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323 | (7) |
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9.1.1 Deterministic Status Scenarios |
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324 | (1) |
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9.1.2 Stochastic Status Scenarios |
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325 | (3) |
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9.1.3 Stochastic Rate Scenarios |
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328 | (2) |
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9.2 Simulation Techniques |
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330 | (10) |
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331 | (1) |
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9.2.2 Simulation Sampling |
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332 | (3) |
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9.2.3 Simulation Probabilities |
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335 | (2) |
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9.2.4 Simulation Prediction Intervals |
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337 | (3) |
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9.3 Investment Pricing Applications |
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340 | (3) |
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9.4 Stochastic Surplus Application |
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343 | (1) |
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9.5 Future Directions in Simulation Analysis |
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344 | (2) |
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346 | (2) |
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348 | (2) |
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350 | (3) |
10 Further Statistical Considerations |
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353 | (22) |
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10.1 Mortality Adjustment Models |
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354 | (7) |
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10.1.1 Linear Mortality Acceleration Models |
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355 | (2) |
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10.1.2 Mean Mortality Acceleration Models |
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357 | (3) |
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10.1.3 Survival-Based Mortality Acceleration Models |
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360 | (1) |
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10.2 Mortality Trend Modeling |
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361 | (3) |
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10.3 Actuarial Statistics |
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364 | (6) |
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10.3.1 Normality-Based Prediction Intervals |
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365 | (1) |
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10.3.2 Prediction Set-Based Prediction Intervals |
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366 | (2) |
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10.3.3 Simulation-Based Prediction Intervals |
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368 | (2) |
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10.4 Data Set Simplifications |
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370 | (1) |
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371 | (1) |
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371 | (2) |
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373 | (2) |
Appendix A: Excel Statistical Functions, Basic Mathematical Functions, and Add-Ins |
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375 | (2) |
Appendix B: Acronyms and Principal Sections |
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377 | (2) |
References |
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379 | (6) |
Symbol Index |
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385 | (4) |
Index |
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