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