Preface |
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xii | |
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1 | (12) |
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1.1 Our Subject and Why It Matters |
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1 | (1) |
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1.2 Players, Roles, and Risk Measures |
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2 | (2) |
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1.3 Book Contents and Structure |
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4 | (3) |
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1.4 What's in It for the Practitioner? |
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7 | (2) |
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9 | (4) |
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2 The Insurance Market and Our Case Studies |
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13 | (14) |
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13 | (2) |
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2.2 Ins Co.: A One-Period Insurer |
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15 | (1) |
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16 | (1) |
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2.4 Examples and Case Studies |
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17 | (8) |
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25 | (2) |
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27 | (134) |
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29 | (34) |
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3.1 Risk in Everyday Life |
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29 | (1) |
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30 | (1) |
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31 | (5) |
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3.4 Representing Risk Outcomes |
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36 | (4) |
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3.5 The Lee Diagram and Expected Losses |
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40 | (14) |
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54 | (6) |
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60 | (3) |
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4 Measuring Risk with Quantiles, VaR, and TVaR |
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63 | (42) |
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63 | (7) |
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70 | (15) |
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4.3 Tail VaR and Related Risk Measures |
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85 | (17) |
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4.4 Differentiating Quantiles, VaR, and TVaR |
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102 | (1) |
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102 | (3) |
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5 Properties of Risk Measures and Advanced Topics |
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105 | (42) |
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5.1 Probability Scenarios |
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105 | (5) |
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5.2 Mathematical Properties of Risk Measures |
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110 | (14) |
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124 | (6) |
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5.4 The Representation Theorem for Coherent Risk Measures |
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130 | (7) |
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5.5 Delbaen's Differentiation Theorem |
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137 | (4) |
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141 | (6) |
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5.A Lloyd's Realistic Disaster Scenarios |
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142 | (1) |
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5.B Convergence Assumptions for Random Variables |
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143 | (4) |
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6 Risk Measures in Practice |
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147 | (10) |
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6.1 Selecting a Risk Measure Using the Characterization Method |
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147 | (1) |
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6.2 Risk Measures and Risk Margins |
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148 | (1) |
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6.3 Assessing Tail Risk in a Univariate Distribution |
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149 | (1) |
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6.4 The Intended Purpose: Applications of Risk Measures |
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150 | (3) |
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6.5 Compendium of Risk Measures |
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153 | (3) |
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156 | (1) |
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7 Guide to the Practice Chapters |
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157 | (4) |
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Part II Portfolio Pricing |
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161 | (146) |
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8 Classical Portfolio Pricing Theory |
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163 | (54) |
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8.1 Insurance Demand, Supply, and Contracts |
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163 | (5) |
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168 | (10) |
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8.3 Accounting Valuation Standards |
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178 | (4) |
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8.4 Actuarial Premium Calculation Principles and Classical Risk Theory |
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182 | (4) |
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8.5 Investment Income in Pricing |
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186 | (3) |
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8.6 Financial Valuation and Perfect Market Models |
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189 | (3) |
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8.7 The Discounted Cash Flow Model |
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192 | (8) |
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8.8 Insurance Option Pricing Models |
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200 | (10) |
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8.9 Insurance Market Imperfections |
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210 | (3) |
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213 | (4) |
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8.A Short- and Long-Duration Contracts |
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215 | (1) |
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8.B The Equivalence Principle |
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216 | (1) |
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9 Classical Portfolio Pricing Practice |
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217 | (16) |
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9.1 Stand-Alone Classical PCPs |
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217 | (6) |
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9.2 Portfolio CCoC Pricing |
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223 | (1) |
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9.3 Applications of Classical Risk Theory |
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224 | (3) |
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9.4 Option Pricing Examples |
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227 | (4) |
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231 | (2) |
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10 Modern Portfolio Pricing Theory |
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233 | (38) |
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10.1 Classical vs. Modern Pricing and Layer Pricing |
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233 | (2) |
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10.2 Pricing with Varying Assets |
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235 | (3) |
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10.3 Pricing by Layer and the Layer Premium Density |
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238 | (1) |
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10.4 The Layer Premium Density as a Distortion Function |
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239 | (6) |
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10.5 From Distortion Functions to the Insurance Market |
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245 | (7) |
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10.6 Concave Distortion Functions |
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252 | (3) |
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10.7 Spectral Risk Measures |
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255 | (4) |
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10.8 Properties of an SRM and Its Associated Distortion Function |
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259 | (2) |
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10.9 Six Representations of Spectral Risk Measures |
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261 | (2) |
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10.10 Simulation Interpretation of Distortion Functions |
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263 | (1) |
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10.11 Learning Objectives |
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264 | (7) |
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265 | (6) |
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11 Modern Portfolio Pricing Practice |
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271 | (36) |
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11.1 Applying SRMs to Discrete Random Variables |
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271 | (4) |
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11.2 Building-Block Distortions and SRMs |
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275 | (5) |
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11.3 Parametric Families of Distortions |
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280 | (5) |
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285 | (7) |
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11.5 Selecting a Distortion |
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292 | (6) |
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11.6 Fitting Distortions to Cat Bond Data |
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298 | (6) |
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11.7 Resolving an Apparent Pricing Paradox |
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304 | (2) |
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306 | (1) |
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Part III Price Allocation |
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307 | (134) |
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12 Classical Price Allocation Theory |
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309 | (30) |
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12.1 The Allocation of Portfolio Constant CoC Pricing |
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309 | (3) |
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12.2 Allocation of Non-Additive Functionals |
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312 | (12) |
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12.3 Loss Payments in Default |
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324 | (2) |
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12.4 The Historical Development of Insurance Pricing Models |
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326 | (11) |
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337 | (2) |
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13 Classical Price Allocation Practice |
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339 | (10) |
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13.1 Allocated CCoC Pricing |
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339 | (8) |
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13.2 Allocation of Classical PCP Pricing |
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347 | (1) |
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348 | (1) |
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14 Modern Price Allocation Theory |
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349 | (48) |
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14.1 The Natural Allocation of a Coherent Risk Measure |
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349 | (16) |
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14.2 Computing the Natural Allocations |
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365 | (4) |
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14.3 A Closer Look at Unit Funding |
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369 | (16) |
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14.4 An Axiomatic Approach to Allocation |
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385 | (7) |
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14.5 Axiomatic Characterizations of Allocations |
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392 | (2) |
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394 | (3) |
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15 Modern Price Allocation Practice |
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397 | (44) |
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15.1 Applying the Natural Allocations to Discrete Random Variables |
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397 | (7) |
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15.2 Unit Funding Analysis |
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404 | (9) |
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15.3 Bodoff's Percentile Layer of Capital Method |
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413 | (8) |
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421 | (18) |
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439 | (2) |
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441 | (52) |
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443 | (6) |
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443 | (1) |
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16.2 Adding Asset Risk to Ins Co. |
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444 | (3) |
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447 | (2) |
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449 | (20) |
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17.1 Time Periods and Notation |
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449 | (1) |
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17.2 Liability for Ultimate Losses |
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450 | (11) |
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17.3 The Solvency II Risk Margin |
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461 | (7) |
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468 | (1) |
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18 Going Concern Franchise Value |
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469 | (8) |
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469 | (3) |
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18.2 The Firm Life Annuity |
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472 | (4) |
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476 | (1) |
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19 Reinsurance Optimization |
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477 | (6) |
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477 | (1) |
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19.2 Evaluating Ceded Reinsurance |
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477 | (4) |
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481 | (2) |
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20 Portfolio Optimization |
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483 | (10) |
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483 | (1) |
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484 | (1) |
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20.3 Dynamic Capital Allocation and Marginal Cost |
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485 | (2) |
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20.4 Marginal Cost and Marginal Revenue |
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487 | (1) |
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20.5 Performance Management and Regulatory Rigidities |
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488 | (2) |
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20.6 Practical Implications |
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490 | (1) |
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491 | (2) |
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493 | (10) |
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A.1 Interest Rate, Discount Rate, and Discount Factor |
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493 | (1) |
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A.2 Actuarial vs. Accounting Sign Conventions |
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493 | (1) |
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494 | (6) |
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A.4 Additional Mathematical Terminology |
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500 | (3) |
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503 | (20) |
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507 | (16) |
Index |
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523 | |