Practical Risk Theory for ActuariesCRC Press, 1 gru 1993 - 576 This classic textbook covers all aspects of risk theory in a practical way. It builds on from the late R.E. Beard's extremely popular book Risk Theory, but features more emphasis on simulation and modeling and on the use of risk theory as a practical tool. Practical Risk Theory is a textbook for practicing and student actuaries on the practical asp |
Spis treści
| 3 | |
| 7 | |
13 Some features of the classical theory | 13 |
14 Notation and some concepts from probability theory | 18 |
2 The number of claims | 30 |
22 The Poisson distribution | 31 |
23 Properties of Poisson variables | 33 |
24 Mixed Poisson claim number variable | 38 |
103 Premiums in practice | 316 |
11 Expenses taxes and dividends | 320 |
112 Taxes | 324 |
113 Dividends | 325 |
12 The insurance process | 327 |
122 Empirical observations | 329 |
123 Business cycles analysis of causes and mechanisms | 333 |
124 Simulation of the insurance process | 343 |
negative binomial distribution | 48 |
26 Variation of risk propensity within the portfolio | 51 |
3 The amount of claims | 55 |
32 Properties of compound distributions | 58 |
33 The claim size distribution | 69 |
34 Claims and reinsurance | 100 |
4 Calculation of a compound claim df F | 119 |
42 Approximate formulae for F | 125 |
5 Simulation | 137 |
52 Random numbers | 138 |
53 Simulation of claim numbers | 141 |
54 Simulation of compoun dvariables | 143 |
55 Outlines for simulation of more complex insurance processes | 147 |
6 Applications involving shortterm claim fluctuation | 155 |
62 Evaluating the capital at risk | 163 |
63 Rules for maximum retention | 170 |
64 An application to ratemaking | 178 |
65 Experiencerating | 179 |
66 Optimal risk sharing | 189 |
PART TWO STOCHASTIC ANALYSIS OF INSURANCE BUSINESS | 209 |
7 Inflation | 211 |
72 Inflation and insurance | 214 |
73 Modelling inflation | 218 |
8 Investment | 226 |
82 Investment returns | 230 |
83 Modelling investment prices and returns | 239 |
84 The Wilkie model | 242 |
85 Other model structures | 250 |
86 Assetliability considerations | 263 |
9 Claims with an extended time horizon | 277 |
92 Claim number process | 278 |
93 Claim amounts | 282 |
94 Simulation of the claim process | 285 |
95 The settlement of claims | 289 |
96 Catastrophes | 305 |
10 Premiums | 310 |
102 Theoretical background | 311 |
13 Applications to longterm processes | 357 |
132 Capital requirements of an insurance company | 363 |
133 Evaluation of an insurers net retention limits | 367 |
14 Managing uncertainty | 369 |
142 Basic equations | 371 |
143 The insurer and the market | 373 |
144 Measuring and managing financial strength | 382 |
145 Corporate planning | 390 |
146 Public solvency control | 397 |
15 Life insurance | 408 |
152 Stochastic cohort approach | 413 |
153 Analysis of the total business | 426 |
16 Pension schemes | 435 |
162 Pension formulae | 436 |
163 Deterministic method sof pension funding | 442 |
164 Stochastic methods for pensions | 447 |
APPENDICES | 452 |
A2 Derivation of the Poisson distribution la w | 454 |
B Polya and Gamma distributions | 459 |
C Asymptotic behaviour of the compound mixed Poisson df | 462 |
D Numerical calculation of the normal df | 463 |
E Derivation of the recursion formula for F | 465 |
F Simulation | 468 |
F2 Normally distributed random numbers | 469 |
F4 Numerical outputs and their accuracy | 470 |
F5 Simulation of the insurance business | 472 |
G Time series | 476 |
G2 Autoregressive process of first order | 479 |
G3 Autoregressive process of second order | 481 |
G4 Generalizations an dvariants | 484 |
H Portfolio selection | 488 |
I Solutions to exercises | 492 |
Bibliography | 514 |
| 526 | |
| 544 | |
Inne wydania - Wyświetl wszystko
Practical Risk Theory for Actuaries C.D. Daykin,T. Pentikainen,Martti Pesonen Ograniczony podgląd - 1993 |
Practical Risk Theory for Actuaries C.D. Daykin,T. Pentikainen,Martti Pesonen Podgląd niedostępny - 1993 |
Kluczowe wyrazy i wyrażenia
actuarial aggregate claim amount analysis applications approach approximation assets assumed calculated cedant's Chapter claim size d.f. claim size distribution coefficient cohort compound mixed Poisson condition cycles Daykin defined denoted derived deterministic dividend yield dividends equation equity estimate evaluation example excess of loss Exercise expected number expected value function factor Figure fluctuation formula gamma distribution increase inflation insurance company Jensen inequality kurtosis liabilities limited expected value loss reinsurance methods mixed Poisson variable mixing variable normal normally distributed number of claims obtained outcomes parameters Pareto Pareto distribution pension Pentikäinen period policies policyholders portfolio premium income probability problem profit quota share random numbers random variable rate of inflation rate of return reinsurance treaty relevant result retention limit risk premium risk theory risk unit run-off safety loading simulation skewness solvency margin solvency ratio standard deviation stochastic stochastic process term variance Wilkie