Index

absolute loss

acceptance–rejection

ACF, see autocorrelation, function

action (in dynamic programming)

additive model

ADP, see dynamic programming, approximate

antithetic sampling

APT, see arbitrage pricing theory

AR, see autoregressive

arbitrage

opportunity

pricing theory

arc (in a network)

ARCH

model

ARIMA

ARMA

asset pricing

asset–liability management

association, linear

autocorrelation

function

sample

partial, see partial autocorrelation

autocorrelogram

autocovariance

autoregressive

conditionally heteroskedastic, see ARCH

integrated moving-average, see ARIMA

model

moving-average, see ARMA

process

backshift operator

balance condition for Markov chains

detailed

global

bandwidth

barrier option, see option, barrier

basis

function

of a lattice

batch method

batching

Bayes’ theorem

Bayesian

computational statistics

estimation

parameter estimation

statistics

view

bequest, utility from

Bernoulli

random variable

trial

beta

distribution

function

variate generation

bias

big-M constraint

binomial

coefficient

distribution

lattice

model

random variable

black swan

Black–Scholes–Merton formula

partial differential equation

world

Boltzmann constant

bond

bootstrap

bootstrapping

bond yields

Box–Jenkins model

Box–Muller method

branching factor

Brownian bridge

BSM, see Black–Scholes–Merton

Buffon’s needle

burn-in

càdlàg function

capital asset pricing model

CAPM, see capital asset pricing model

cardinality constraint

Cartesian product

CDF, see cumulative distribution function

central limit theorem

for quantiles

chain rule

chance-constrained model

chi-square

distribution

noncentral

random variable

test

variable

Cholesky

factor

factorization

CIR, see Cox–Ingersoll–Ross

code vectorization

coefficient of determination

coefficient of variation

collocation

method

node

combinatorial optimization

common random numbers

complete market

concave

function

optimization problem

problem

concordance

conditional

density

expectation

Monte Carlo

probability

value-at-risk, see also value-at-risk, conditional

variance

conditioning

confidence interval

half-length

confidence level

conjugate family (of priors)

conjugate prior

consumption–saving problem

continuation

region

value

continuous-time model

continuously compounded interest rate

contour plot

control variable

control variate

convex

function

polyhedral

strictly

hull

optimization

optimization problem

set

convexity

cooling schedule

copula

t

estimation

Gaussian

normal

product

Student’s t

theory

correlation

coefficient

instantaneous

negative

Pearson’s

sample

testing significance

cost-to-go

counting process

covariance

matrix

sample

coverage (in confidence intervals)

covered position

Cox–Ingersoll–Ross model

Cramér–Rao bound

credible interval

cross-entropy method

cross-sectional

dependence

dependency

model

cumulant generating function

cumulative distribution function

empirical

joint

curse of dimensionality

CV@R, see value-at-risk, conditional

decision rules

decision variable

binary

logical

semicontinuous

default

degrees of freedom

delta hedging

density

candidate

instrumental

target

derivative

financial

over-the-counter

derivative-free method

destandardization

deterministic equivalent

detrending

diagonal model

differencing

second-order

differential equation

digital shift

dimensionality reduction

direction number

discount factor

subjective

discrepancy

star

discrete-event model

discrete-time model

discretization error

distribution, see also specific distribution

cumulative function

beta

bimodal

binomial

conditional

cumulative function joint

discrete empirical

elliptical

lognormal

multivariate normal

right-skewed

skewed

uniform

disturbance

diversification

DP, see dynamic programming

drift

duration

dynamic programming

approximate

numerical

stochastic

early exercise

boundary

efficient market hypothesis

eigenvalue

eigenvector

elliptical distribution

EMH, see efficient market hypothesis

empirical distribution

endogenous uncertainty

envelope theorem

epsilon-greedy policy

equilibrium condition

Erlang

distribution

random variable

error

absolute

discretization

relative

sampling

estimation error

estimator

biased

consistent

controlled

efficient unbiased

high-biased

low-biased

point

stratified

unbiased

Euler discretization scheme

Euler–Maruyama discretization scheme, see Euler

excess return

exclusive OR

exogenous uncertainty

expected value

of a function

explicit scheme

exploitation

exploration

exponential

distribution

memoryless property

random variable

variable

exponential tilting

exponential twisting, see exponential tilting

F distribution

factor analysis

factor model

factorial

factorization, Cholesky

fat solution

fat tail

Faure sequence

feasible

region

set

feedback policy

Feynman–Ka formula

financial asset

finite difference

central

forward

firefly algorithm

frequentist probability

Fubini theorem

function

2-increasing

grounded

indicator

piecewise linear

functional equation

fundamental pricing equation

gamma

distribution

function

and factorials

random variable

GARCH

Gauss–Hermite

quadrature

Gaussian

copula

distribution

process

quadrature, see also quadrature, Gaussian

white noise

GBM, see geometric Brownian motion

generalized autoregressive conditionally heteroskedastic model, see GARCH

generalized feedback shift registers

generalized inverse

genetic algorithm

geometric

distribution

random variable

geometric Brownian motion

bidimensional

multidimensional

GFSR, see generalized feedback shift registers

Gibbs sampler

global optimization

goodness of fit

test

graph optimization

Gray code

grounded function

half-length (of a confidence interval)

Halton sequence

Hardy–Krause variation

hedging strategy

Hessian matrix

Heston model

heteroskedasticity

homoskedasticity

hypercube

hypothesis

alternative

null

i.i.d. (independent and identically distributed)

implicit scheme

importance sampling

income uncertainty

incomplete market

increment

stationary and independent

independence

vs. lack of correlation

independent increment

indicator function

inferential statistics

inner product

integer programming

integral

multidimensional

Riemann

stochastic

integrating factor

integration error

interest rate

continuously compounded

instantaneous

modeling

interior point methods

interpolation

piecewise linear

intrinsic value

inverse problem

inverse transform method

It

isometry

lemma

process

stochastic differential equation

stochastic integral

Jacobian

determinant

matrix

Jarque–Bera test

Jensen’s inequality

joint

probability density function

probability mass function

jump

jump–diffusion process

Kendall’s tau

kernel density

kernel-based estimation

Koksma–Hlawka theorem

Kolmogorov–Smirnov

measure of fit

test

Korobov point set

kurtosis

excess

labor income

lack of memory (exponential distribution)

Lagrange multiplier

Lagrange polynomial

Lagrangian function

large numbers

strong law of

Latin hypercube sampling

lattice

binomial

calibration

generator

projection regular

rank-r rule

structure in LCG

law of iterated expectations

law of one price

LCG, see linear congruential generator

least-squares

nonlinear problem

Levenberg–Marquardt method

Lévy flight

Lévy–It decomposition

Lévy process

likelihood

function

log-function

method of maximum

likelihood ratio

derivative estimation

method

linear congruential generator

linear programming

canonical form

mixed integer

standard form

linear regression

probabilistic view

linearity

local improvement

local maxima

local search

best-improving

first-improving

log-likelihood function

log-return

logarithm

lognormal

distribution

random variable

longitudinal

dependence

model

loss function

low-discrepancy sequence

scrambled

LP, see linear programming

lurking variable

margin

marginal

cumulative distribution function

density

distribution

probability density function

market

complete

incomplete

market portfolio

Markov

chain

aperiodic

continuous-time

discrete time

discrete-time

irreducible

long-run distribution

time reversible

decision process

process

Markov chain Monte Carlo

Markovian

dynamic system

process

Markowitz portfolio model

mathematical programming

matrix

positive definite

positive semidefinite

transposition

maximization problem

maximum-likelihood

estimation

estimator

method

properties of estimator

MCMC, see Markov chain Monte Carlo

MDP, see Markov decision process

mean reversion

mean reverting process

mean–risk decision model

mean–variance

efficient portfolio

portfolio optimization

median

memoryless property (exponential distribution)

Mersenne

number

twister generator

metaheuristic

metamodel

metamodeling

method of batches

method of moments

Metropolis–Hastings algorithm

blockwise

MILP, see linear programming, mixed integer

Milstein discretization scheme

MLE, see maximum-likelihood estimator

mod (math operator)

mode

model calibration

model identification

modulus (in random number generation)

moment

first-order

sample

second-order

moment generating function

normal distribution

moment matching

monomial basis

monotonicity

monotonicity (requirement for variance reduction)

Monte Carlo integration

Monte Carlo simulation as an integration problem

structure of

moving-average model

moving-average process

multiplicative model

multiplier (in random number generation)

naked position

neighborhood structure

Nelder–Mead method

network optimization

newsvendor problem

Newton’s method

Newton–Cotes quadrature formula

node (in a network)

node (in a quadrature formula)

nonanticipativity

noncentrality parameter

nonconvex

optimization

optimization problem

set

nonlinear least squares

nonlinear programming

nonparametric test

nonstationary process

normal

bivariate distribution

copula

distribution

mixture of

standard

moment generating function

multivariate conditional distribution

multivariate variable

random variable

standard distribution

standard random variable

standard variable

variate

numerical integration, see quadrature

numerical optimization

objective function

OLS, see ordinary least squares

optimal control, continuous-time

optimality equation

optimization

combinatorial

constrained problem

finite-dimensional

model

nonconvex

unconstrained problem

under uncertainty

option

American-style

as-you-like-it

Asian

arithmetic average

geometric

geometric average

Asian-style

barrier

Bermudan-style

call

chooser

continuation value

deeply out-of-the-money

delta

digital call

down-and-in put

down-and-out put

European-style

exchange

gamma

greek

holder

in-the-money

intrinsic value

lookback

lookback call

multidimensional

out-of-the-money

path dependent

path-dependent

pricing

sensitivity

spread

theta

vanilla call

vega

writer

order statistics

ordinary least squares

Ornstein–Uhlenbeck process

orthodox statistics

orthogonal

matrix

polynomial

overfitting

overflow

PACF, see partial autocorrelation function

panel

data

model

parameter estimation

Bayesian

parity

for barrier options

put–call

partial autocorrelation function

sample

partial differential equation

particle swarm optimization

passive portfolio management

pathwise derivative estimation

pathwise differentiation

PCA, see principal component analysis

PDE, see partial differential equation

PDF, see probability density function

penalty function

periodicity (in random number generators)

permanent shock

perturbation analysis

PMF, see probability mass function

point estimate

point estimator

Poisson

distribution

process

compound

inhomogeneous

random variable

polar

coordinate

rejection

policy iteration

polyhedral set

polyhedron

polynomial

interpolation

primitive

polynomial regression

portfolio

benchmark

compression

tracking

position

covered

naked

positive homogeneity

post-decision

value function

posterior

density

distribution

predictor-corrector method

prime number

principal component

principal component analysis

prior

density

distribution

probability

density function

joint

mass function

marginal

measure

risk-neutral

process

adapted

standard Wiener

Wiener

nondifferentiability of

product rule

projection regular (lattice)

pseudorandom, see also random number

number generator

state

PSO, see particle swarm optimization

put–call parity

Pythagorean theorem

Q-factor

Q-learning

QP, see quadratic programming

Q-Q plot

quadratic form, convex

quadratic programming

quadrature

formula

closed

composite

Gauss–Laguerre

Gauss–Legendre

Newton–Cotes

open

order

Gauss–Hermite

Gaussian

product rule

trapezoidal rule

quantile

estimated

estimation

of normal distribution

quantum PSO

quasi–Monte Carlo

quasi–random number

Radon–Nikodym derivative

random number, see also pseudorandom

random number generator

combined

generalized feedback shift registers

Mersenne twister

multiple recursive

multiplicative

separate stream

Tausworthe

Wichman–Hill

random sample

random shift

random shock

random variable, see also specific random variable

continuous

discrete

independent

jointly continuous

lognormal

normal

standard normal

uniform

random walk

rank correlation

Rastrigin function

rate

continuously compounded

risk-free

recourse

function

matrix

simple

variable

rectangle rule

recursive equation

recursive functional equation

rejection region

rejection sampling, see acceptance-rejection

replicating portfolio

replication

residual

response surface

return

continuously compounded

rate of

Richardson extrapolation

risk

aversion

idiosyncratic

management

measure

coherent

specific

systematic factor

risk-neutral

measure

option pricing

pricing

probability measure

SACF, see autocorrelation function, sample

sample

correlation

covariance

mean

partial autocorrelation function

path

variance

sampling vs. simulation

scale parameter

scatterplot

scenario

extreme

generation

tree

score function

scrambling

Faure–Tezuka

of a low-discrepancy sequence

Owen

SDE, see stochastic differential equation

seasonality

seed

setting in random number generators

semiannual compounding

semicontinuous variable

sensitivity estimation

shape parameter

Shapiro–Wilk test

shift (in random number generation)

short rate

short selling

shortest path problem

shortfall probability

simplex

algorithm

method

search

Simpson’s rule

simulated annealing

generalized

simulation-based optimization

skewness

negative

Sklar’s theorem

small world PSO

Sobol sequence

SP, see stochastic programming

SPACF, see partial autocorrelation function, sample

Spearman’s rho

spline

cubic

natural

square-root diffusion

square-root matrix

square-root rule

stability

in sample

out of sample

stable distribution

standard deviation

of return

standard normal distribution

standard Wiener processes

standardization

star discrepancy

state transition

equation

function

state variable

post-decision

stationary and independent increments

stationary increment

steepest descent

stochastic calculus

stochastic differential

stochastic differential equation

stochastic dynamic optimization

stochastic dynamic programming

stochastic integral

stochastic optimization

stochastic process

mean reverting

nonstationary process

predictable

stationary

weakly stationary

stochastic programming

multistage with recourse

two-stage

with chance constraints

with recourse

stochastic search

stochastic volatility

stop-loss hedging

stopping time

strategic oscillation

stratification

stratified sampling

stream, in random number generators

strike price

Student’s t

distribution

multivariate distribution

random variable

subadditivity

subjective

knowledge

probability

sufficient statistics

surface plot

tabu search

tail dependence

tail risk

Taylor expansion

t distribution multivariate

term structure of interest rates

TEV, see tracking error variance

tilting parameter

time bucket

time consistency

time series

analysis

model

total probability theorem

tracking error variance

tracking portfolio

transaction cost

transient phase

transition

density

kernel

matrix

probability

matrix

transitory shock

translation invariance

transposition

uncorrelated variables

uniform

random variable

unit hypercube

unk-unks (unknown unknowns)

utility

expected

function

quadratic

utility function

logarithmic

power

value function

value-at-risk

absolute

conditional, see also conditional, value-at-risk

historical

relative

Van der Corput sequence

VAR, see vector autoregressive model

V@R, see value-at-risk

variance

of a sum of random variables

variance reduction

Vasicek model

vector autoregressive model

vector transposition

volatility

cluster

stochastic

volume risk

weakly stationary process

wealth

Weierstrass theorem

weight function

weights (in a quadrature formula)

white noise

Gaussian

whitening

Wichman–Hill generator

Wiener process

bidimensional

correlated

differential

generalized

lack of differentiability

standard

yield curve

zero-coupon bond