Index
Page numbers followed by an "n" indicate footnotes.
accumulated winnings in law of large
numbers, 351-352
actuarial present value, 305
actuarial science, 6-9
addition with random variables, 124-125
additive rates, 434-435
adverse selection problem, 9
ageless property, 207n
AGM (arithmetic-geometric means)
inequality, 46-47, 133-134
alcohol study example, 61-64
Alembert, Jean Le Rond d', 3n
American options, 302
annuities, 36, 309-311
arbitrage opportunities, 10
areas under curves, 98-99
arithmetic expectations, 131
deviation from, 143
and geometric
connections with, 45-46
inequality with, 46-47
relationship between, 138-139
in growth, 44-47
properties of, 139-141
arithmetic-geometric means (AGM)
inequality, 46-47, 133-134
arithmetic operations
beta distribution, 262
binomial distribution, 191-192
DeMoivre distribution, 243
exponential distribution, 223-224
gamma distribution, 229-230
geometric distribution, 208
lognormal distribution, 258
negative binomial distribution,
204
normal distribution, 249
Pareto distribution, 235
Poisson distribution, 197-198
on random variables, 124-125
Weibull distribution, 238
association
covariance for, 341-342
degrees of, 342-343
associative laws for sets, 86
asymmetry, informational
Bayes' theorem in, 72-75
in insurance, 57
automobile tire lifetimes, Weibull
distribution for, 238
axiomatic approaches, 4
balanced dice, 19
bar charts, 22
batteries
failures, Weibull distribution for,
238-239
in series and parallel systems,
313-316
Bayes, Thomas, lln
Bayes' theorem, 58
distributional form, 123-124
examples, 73-75
for insurance, 57, 72-73
Bayesian interpretation of probability,
11-13
beneficiaries, life insurance, 304
Bernoulli random variables, 192
beta distribution
arithmetic operations with, 262
definition and interpretation, 260-261
examples, 263-265
mean, variance, and higher moments
for, 261
probability calculations for, 261-262
probability density function for, 261
relationship with other distributions,
262-263
beta function
definition, 428
incomplete, 262, 429
biased coins, 3n
bids, construction, transformations for,
316-317
binomial distribution
arithmetic operations with, 191-192
definition and interpretation of, 187-190
mean, variance, and higher moments
for, 190-191
negative. See negative binomial
distribution
probability calculations for, 191
probability mass function for, 190
relationship with other distributions,
192, 262-263
birthday problem, 89
births, negative binomial distribution for,
204-205
bivariate density, 106, 116, 249
bivariate distributions, 29, 104-113
bond mutual funds, model for. See
Markowitz investment portfolio
selection model
call options, 302
capital allocation in insurance, 8-9
Capital Asset Pricing Model (CAPM), 396
derivation of, 412
observations on, 412-414
statement of, 411-412
capital markets in financial engineering,
10
caps, insurance with, 368-372
combination contracts, 300-302
excess-of-loss contracts, 297-298
limited excess-of-loss contracts,
298-299
option contracts, 302-303
proportional insurance contracts, 300
Cardan, Girolamo, 2
Cauchy distribution, 357-358
means in, 319
in normal distributions, 251
441
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