Index

arrival time

14.2

Asian crisis

11. | 11.2.2 | 11.4

asset return

1.5

asset returns

1.1 | 3.6

bankruptcy

10. | 10. | 10.1

Basel Capital Accord

Basel I: 10.2
Basel II: 10.1 | 10.2 | 10.2

basis function

Bates' model

no title

beta function

13.4.1

Black Monday

1.5

Black-Scholes formula

5.1 | 5.2 | 7.1 | 7.4 | 8.2

bond

callable: Mortgages
catastrophe: see CAT bond
defaultable: 4.1.3
non-callable: Mortgages
rating: 10.1

Brownian motion

16.1 | 16.2.3

arithmetic: 15.6.3
fractional: 17.1 | 17.2
geometric: 7.2 | 8.2 | 8.2.2

burnout

Mortgages | 9.3.2.2

Burr distribution

see distribution

Capital Asset Pricing Model (CAPM)

20.2.2

capital market

4.1

CAT bond

4. | 4.1.1 | 4.1.2 | 4.4

coupon: 4.4
coupon-bearing: 4.4
maturity: 4.1
premium: 4.1
pricing: 4.1.3
principal: 4.1
zero-coupon: 4.1.3 | 4.4

catastrophe

bond

see CAT bond

data

14.3.1 | 16.3

seasonality: 4.3
trend: 4.3

futures

see derivative

natural

4.1.1 | 13.5

option

see derivative

Chambers-Mallows-Stuck method

1.3

change of measure

17.3

characteristic function

1.2.1 | 8.2.1 | 8.2.3 | 8.4

Cholesky factorization

5.5.1

claim

correlated: 17.1
severity: 14.1

claim arrival process

see process

claim surplus process

see process

classification

10. | 10.1

clustering

cluster center: 11.3.1
fuzzy: 11. | 11.3.1 | 11.3.1
fuzzy set: 11.3.2
membership function: 11.3.2
Takagi-Sugeno approach: 11.3.2

cointegration

11.1 | 11.2.1

collective risk model

14.1 | 18. | 18.3 | 19.1

collective risk theory

16.1

composition method

see method

consumer price index

contingent claim

7.3

copula

2. | 2.2.1 | 2.2.1 | 2.2.1 | 3.3.3

: 3.7
Ali-Mikhail-Haq: 2.2.1 | 3.3.1
Archimedean: 3.3.1 | 3.3.1 | 3.3.1
Clayton: 2.2.1 | 2.2.2 | 3.3.1
Farlie-Gumbel-Morgenstern: 2.2.1 | 2.2.2
Frank: 2.2.1 | 2.2.1 | 2.2.2
Galambos: 2.2.3 | 2.2.4
Gaussian: 2.2.1
Gumbel: 2.2.1 | 2.2.3 | 2.2.4
Gumbel II: 2.2.3 | 2.2.4
Gumbel-Hougaard: 3.3.1

correlation

7.4 | 7.4.1

Cox process

see process

credit risk

14.1

critical value

13.4.2

cumulant

generating function: 20.5.1

data envelopment analysis (DEA)

12.2 | 12.2.1 | 12.3

efficient level: 12.2.1

dataset

Danish fire losses: 13.5 | 14.3.2 | 19.3
Property Claim Services (PCS): 13.5 | 14.3.1 | 15.1 | 18.2.3.0.1

Datastream

DAX index

5.1 | 5.2

deductible

13.4.1 | 19.

disappearing

19.2.5

premium: 19.3.1 | 19.3.2 | 19.3.3 | 19.3.4 | 19.3.5 | 19.3.6

fixed amount

13.4.3 | 19.2.2

premium: 19.3.1 | 19.3.2 | 19.3.3 | 19.3.4 | 19.3.5 | 19.3.6

franchise

19.2.1

premium: 19.3.1 | 19.3.2 | 19.3.3 | 19.3.4 | 19.3.5 | 19.3.6

limited proportional

19.2.4

premium: 19.3.1 | 19.3.2 | 19.3.3 | 19.3.4 | 19.3.5 | 19.3.6

payment function

19.2

proportional

19.2.3

premium: 19.3.1 | 19.3.2 | 19.3.3 | 19.3.4 | 19.3.5 | 19.3.6

default

10.1

probability: 10.2
probability of: 10.1

derivative

4.1 | 7.3

call option

catastrophe futures

4.1.2

catastrophe option

4.1.1 | 4.1.2

delta

7.4 | 9.2.2.3

dual delta

European option

5.2 | 5.2

Gamma

Greeks

rho: 7.3.1
spot delta: 7.3.1

insurance

maturity

see maturity

prepayment option

Mortgages

American: 9.2.1

put option

risk reversal

7.4.2

strike price

5.1 | 5.2

vanilla option

9.3.3

European: 7.3

vega

7.3.1 | 9.3.3

vol of vol

7.2 | 7.4.1

volga

dimension reduction

5.1

disappearing deductible

see deductible

discriminant analysis

10.1 | 10.1

distribution

$\theta$ -stable

$\alpha$ -stable

16.1

Bernoulli

17.2

Burr

4.2 | 4.3 | 13.3.4 | 13.4.1 | 13.4.3 | 15.3.12 | 16.3 | 19.3.3

chi-squared ( $\chi^2$ )

13.3.6

claim amount

4.3

Cobb-Douglas

13.3.1

compound geometric

15.2

compound mixed Poisson

18.3.4

compound negative binomial

18.3.4

compound Poisson

18.3.3 | 20.4.1 | 20.4.2

conditional excess

2.1.2 | 2.1.3 | 2.1.3

elliptically-contoured

Erlang

13.3.6

exponential

4.3 | 13.3.2 | 13.3.3 | 13.3.5 | 13.3.6 | 13.4.1 | 13.4.1 | 13.4.3 | 14.2.2 | 15.3.12 | 16.2.1

memoryless property: 13.3.2 | 13.4.1

extreme value

multivariate: 2.2.3

finite-dimensional

17.2

Fréchet

gamma

4.3 | 13.3.3 | 13.3.6 | 13.4.1 | 13.4.3 | 15.3.4 | 18.2.3.0.2 | 18.3.4 | 19.3.5 | 20.5.4

generalized extreme value

generalized Pareto

2.1.2

geometric

15.2 | 20.5.8

Gumbel

heavy-tailed

7.2 | 13.3.3 | 13.3.4 | 15.1.1 | 16.1 | 16.3

hyperbolic

3.3.2 | 7.2

infinitely divisible

13.3.1

inverse Gaussian

15.6.3

Lévy stable

light-tailed

15.1.1

adjustment coefficient: 15.1.1
Lundberg exponent: 15.1.1

log-normal

4.3 | 13.3.1 | 13.4.1 | 13.4.3 | 18.2.3.0.1 | 19.3.1

logistic

loss

see loss distribution

mixture

13.3.3

mixture of exponentials

4.3 | 13.3.7 | 13.4.3 | 15.3.12 | 19.3.6

negative binomial

13.3.6 | 18.3.4

normal

3.2 | 3.3.2 | 5.2 | 10.1 | 16.1 | 20.1

of extremum

Pareto

2.1.1 | 2.1.2 | 4.2 | 4.3 | 13.3.3 | 13.3.4 | 13.4.1 | 13.4.3 | 15.3.12 | 19.3.2

Pareto type II

2.1.2

Pearson's Type III

13.3.6

Poisson

14.2.1 | 18.3.3

power-law

4.1.3

shifted gamma

18.3.2

stable

see stable distribution | 2.1.1

stable Paretian

Student

3.2 | 3.3.2

subexponential

15.3.11 | 20.5.7

convolution square: 15.3.11

transformed beta

15.3.12

translated gamma

18.3.2

truncated-Pareto

20.4.2 | 20.4.2 | 20.7.1

uniform

13.3.2 | 13.4.2

Weibull

2.1.1 | 4.3 | 9.3.2.2 | 12.2.2 | 13.3.5 | 13.4.1 | 13.4.3 | 15.3.12 | 19.3.4

with regularly varying tail

15.3.11

distribution function

empirical: 13.2 | 13.4.2

dividend

fixed: 20.6.1 | 20.7.1
flexible: 20.6.2 | 20.7.3

domain of attraction

16.1 | 16.2.3 | 16.3 | 16.3.3

doubly stochastic Poisson process

see process

Dow Jones Industrial Average (DJIA)

1.5 | 1.5

eigenfunction

5.4

eigenvalue

5.4

elliptically-contoured distributions

empirical distribution function

see distribution function

empirical risk

10.1

error correction model

11.1 | 11.2.1

vector: 11.2.1

estimation

statistic minimization: 13.5
statistic minimization: 19.4
maximum likelihood: 13.5

EUREX

European Central Bank

11.1

expected risk

10.1 | 10.1

expected shortfall

2.1.3 | 13.4.1

expected tail loss

2.1.3

exponential distribution

see distribution

extreme event

1.1

extreme value

filtration

finite difference approach

9.2.2.3

Fisher-Tippet theorem

fixed amount deductible

see deductible

foreign exchange

7.3 | 7.4

Fourier basis

5.3 | 5.3 | 5.4.1

Fourier transform

1.2.1 | 8.3 | 8.3

fast (FFT)

8.1 | 8.3 | 8.3 | 8.3 | 8.3

option pricing: 8.3 | 8.4

fractional Brownian motion

see Brownian motion

franchise deductible

see deductible

Fredholm eigenequation

5.4

free boundary problem

9.2.2.3

free disposal hull (FDH)

12.2 | 12.2.2 | 12.4

efficiency score: 12.2.2
efficient level: 12.2.2

function

basis: see basis function
beta: see beta function
characteristic: see characteristic function
classifier: see Support Vector Machine (SVM)
distribution: see distribution function
frontier: see production
Heaviside: see Heaviside function
kernel: see Support Vector Machine (SVM)
limited expected value: see limited expected value function
mean excess: see mean excess function
mean residual life: see mean residual life function
membership: see clustering
moment generating: see moment generating function
production: see production
slowly varying at infinity: 16.3.1

functional data analysis

5. | 5.3

gamma distribution

see distribution

gamma function

incomplete: 13.3.6 | 13.4.1
standard: 13.3.3

generalized eigenequation

5.5 | 5.5.1

goodness-of-fit

1.5 | 13.1 | 14.3.1

half-sample approach

13.4.2

Heath-Jarrow-Morton approach

9.2.2.1

Heaviside function

9.3

hedging

Heston's model

7. | 7.2 | no title

Hill estimator

1.4.1

homogeneous Poisson process (HPP)

see process

hurricane

implied trinomial trees

see ITT

implied volatility

5. | 5.1 | 7.1 | 7.4 | 8.2 | 8.4 | 8.4 | 8.4 | 9.3.3

surface: 5.1 | 5.1 | 5.2 | 8.4 | 21.3.4

incomplete market

7.1 | 8.2.1

index of dispersion

14.2.3

individual risk model

18. | 18.2 | 19.1

inflation rate

11.1

initial

capital: 14.1 | 16.1
risk reserve: 16.1
variance: 7.3.1 | 7.4 | 7.4.1

insurance

policy: 16.1
portfolio: 14.1 | 15.1 | 18.2 | 18.3 | 20.2.1
risk: 14.1 | 15.1
securitization: 4.1.2

insurance-linked security (ILS)

4.1

indemnity trigger: 4.1
index trigger: 4.1
parametric trigger: 4.1

intensity

see process

intensity function

see process

inter-arrival time

14.2 | 14.2.2 | 17.2

inter-occurrence time

13.3.2

interest

rate

11.2.2 | 11.3.4

effect: 11.3.4
elasticity: 11.4
long-term: 11.3.4

inverse transform method

see method

investment

20.

ITT

jump-diffusion model

7.1 | 7.4.2

Karush-Kuhn-Tucker conditions

Laplace transform

13.3.2 | 13.3.2 | 15.2

inversion: 15.2.4

leverage effect

8.2.2

limited expected value function

13.4.3

limited proportional deductible

see deductible

linear interpolation

local polynomial estimator

log-normal distribution

see distribution

logit

10.1 | 10.1

London Inter-Bank Offer Rate (LIBOR)

4.4

long-run variance

7.2 | 7.4 | 7.4.1

Lorenz curve

10.5

loss distribution

4.3 | 13. | 15.1

analytical approach: 13.1
curve fitting: 13.1
empirical approach: 13.1 | 13.2
moment based approach: 13.1

lower tail-independence

3.3.1

martingale

8.2.1 | 17.3

maturity

5.1 | 5.1 | 9.1 | 9.2.1 | 10.2

time to: 5.1 | 5.2

MD*Base

8.4

Mean Absolute Error (MAE)

4.3 | 8.4

mean excess function

13.4.1 | 13.4.3 | 14.3.1

mean residual life function

13.4.1

mean reversion

7.4 | 7.4.1 | 8.2.2

Mean Squared Error (MSE)

4.3 | 8.4

mean value function

4.3 | 14.3.1

Merton's model

no title

method

composition: 13.3.7
integration: see algorithm
inverse transform: 13.3.2 | 13.3.3 | 13.3.4 | 13.3.5
least squares: 4.3 | 14.3.1
Newton-Raphson: 5.2 | 15.1.1
of characteristic functions: 7.3
rejection: see algorithm
thinning: see algorithm

minimum-volume ellipsoid estimator

3.4

mixed Poisson process

see process

mixture of exponential distributions

see distribution

modeling dependence

2.2.1

moment generating function

13.3.1 | 15.1.1 | 18.1 | 18.3.1

monetary policy

11. | 11.1

monetary union

11.

money demand

11. | 11. | 11.2.2

Indonesian: 11. | 11.3.4
M2: 11.
nominal: 11.1
partial adjustment model: 11.1

moneyness

Monte Carlo

method: 1.5 | 9.3.1 | 15.3.12 | 15.6.1
simulation: 4.1.3 | 8.4 | 8.4 | 13.4.2 | 15.1 | 15.6.1 | 18.3.5.0.1

mortgage

9.1 | Mortgages | 9.2.1

callability: Mortgages | 9.2.2.1 | 9.3.3
optimally prepaid: 9.1 | 9.2.2.2 | 9.2.2.3

mortgage backed security (MBS)

9. | 9.1

valuation: 9.3

multivariate GARCH

2.2.5

multivariate trimming

3.4

natural catastrophe

see catastrophe

neural network

10. | 10.1

non-homogeneous Poisson process (NHPP)

see process

nonparametric regression

normal distribution

multivariate: 3.7

normal power formula

20.3.1

operational risk

14.1 | 15.1 | 18.

operational time scale

15.1

optimal stopping problem

9.2.2.2

Panjer recursion formula

20.5.8

Pareto distribution

see distribution

periodogram

14.3.1

Pickands constant

17.3

point process

see process

Poisson process

see process

policy

flexible dividend: 20.1

Pollaczek-Khinchin formula

15.2 | 15.3.12 | 20.5.7

power-law tail

premium

13.4.3 | 14.1 | 14.2.1 | 14.2.2 | 14.2.5 | 16.1 | 18. | 19.2 | 20. | 20.1 | 20.2.1 | 20.3.1 | 20.5.1 | 20.5.1 | 20.5.5 | 20.5.6 | 20.6.1 | 20.7.2

$\sigma^2$ -loading principle

$\sigma$ -loading principle

balancing problem

20.3.3

exponential

18.1 | 18.2.2 | 18.2.3.0.2 | 18.3.1 | 18.3.2 | 18.3.3 | 18.3.4 | 18.3.5.0.2

marginal

20.3.2

normal approximation

18.2.2 | 18.3.2

pure risk

18.1 | 18.2.1 | 18.3.1 | 19. | 19.2

with safety loading: 18.1

quantile

18.1 | 18.2.2 | 18.2.3.0.1 | 18.3.1 | 18.3.3 | 18.3.4 | 18.3.5.0.1 | 20.2.1

standard deviation principle

translated gamma approximation

18.3.2

variance principle

whole-portfolio

with safety loading

18.2.1 | 18.3.1

with standard deviation loading

18.2.1 | 18.3.1

with variance loading

18.2.1 | 18.3.1

zero utility principle

premium function

see premium

prepayment

optimal frontier: 9.2.2.3
parametric specification: 9.3.2
refinancing: 9.3.2.2
structural: 9.3.2.1

prepayment policy

9.1 | 9.3

early prepayment: 9.2.1
interest rate: 9.1 | Mortgages
optimality: 9.1 | 9.2 | 9.3

principal

9.1 | Mortgages | 9.2.1

principal components analysis (PCA)

5.1 | 5.4

common

5.6

functional

5.1 | 5.4 | 5.4

smoothed

5.5 | 5.5.1

roughness penalty: 5.5 | 5.5

probability space

probit

10.1 | 10.1

process

aggregate loss

4.2 | 14.1 | 15.5 | 20.1

claim arrival

4.3 | 14.1 | 14.2

claim surplus

15.1 | 15.3.6 | 20.5.7

compound Poisson

15.5

counting

16.2

Cox

14.2.4

intensity process: 15.1

doubly stochastic Poisson

14.2.4

homogeneous Poisson

14.2.1 | 14.2.2 | 14.2.2 | 14.2.3

mixed Poisson

14.2.3

non-homogeneous Poisson

14.2.2 | 14.2.4

Ornstein-Uhlenbeck

8.2.2 | 9.2.2.1

point

4.1.3 | 14.1 | 14.1 | 15.1 | 16.1

Poisson

13.3.2 | 15.1 | 15.1 | 16.2.1

compound: 8.2.1 | 8.2.3 | 8.2.3
cumulative intensity function: 4.3 | 14.3.1
doubly stochastic: 4.1.3 | 4.2
homogeneous: 8.2.1
intensity: 14.2.1 | 15.1 | 16.2.1
intensity function: 4.2 | 14.2.2
linear intensity function: 14.3.2
non-homogeneous: 4.1.3 | 4.2
periodic intensity: 14.2.2
rate: 14.2.1
rate function: 14.2.2
sinusoidal intensity function: 14.3.1
stochastic intensity: 4.1.3

predictable bounded

progressive

renewal

4.3 | 14.2.5 | 16.2 | 16.2.3 | 16.3 | 17.2

risk

see risk process | 20.1

self-similar

stationary

variance

Wiener

production

frontier function: 12.1
function: 12.1
input efficiency score: 12.1 | 12.1
output efficiency score: 12.1 | 12.1
set: 12.1 | 12.1
unit: 12.1

productivity analysis

12.

data envelopment analysis

see data envelopment analysis (DEA)

free disposal hull

see free disposal hull (FDH)

input requirement set

12.1

nonparametric

12.

hull method: 12.2

output corresponding set

12.1

Property Claim Services (PCS)

4.1 | 4.3 | 13.5

proportional deductible

see deductible

Public Securities Association

9.3.2.1

pure risk premium

see premium

quantile

9.3.2.2

sample: 14.3.1

quantile line

sample: 14.3.1

queuing theory

15.3.8 | 15.3.9

rate of mean reversion

7.2

rate of return

20.2 | 20.6 | 20.7

rating

10.1 | 10.1 | 10.2 | 10.2 | 10.2

raw moment

13.3.1 | 13.3.2

reinsurance

4.1 | 14.1 | 20. | 20.4 | 20.7 | 20.7.2

excess of loss: 20.4.1

renewal process

see process

retention

19.1 | 20.1

limit: 20.4.1

returns to scale

constant: 12.1
non-increasing: 12.1

risk aversion

18.2.3.0.2

Risk Based Capital (RBC)

20.2.1

risk classification

10.2

risk model

collective: see collective risk model
individual: see individual risk model
of good and bad periods: 17.

risk process

14. | 14.1 | 15.1 | 16.1

modeling

14.

simulation

14.3

stable diffusion approximation

16.

weak convergence

to $\alpha$ -stable Lévy motion: 16.3.1
to Brownian motion: 16.2.1

risk-neutral measure

8.2.1

RiskCalc

10.1 | 10.1 | 10.5

ruin probability

14.1 | 15. | 16.2.2 | 17.1 | 20.7

4-moment gamma De Vylder approximation

15.3.7 | 15.4

adjustment coefficient

Beekman-Bowers approximation

15.3.4 | 15.3.5 | 20.5.4 | 20.7.1

corrected diffusion approximation

15.6.4

Cramér-Lundberg approximation

15.3.1 | 15.4 | 15.6.2 | 20.5.3

criterion

20.5 | 20.6

De Vylder approximation

15.3.6 | 15.4 | 20.5.6 | 20.7.1

diffusion approximation

15.6.3 | 20.5.5

exact

exponential claim amount: 15.2.2 | 15.5.1
gamma claim amount: 15.2.3
mixture of exponentials claim amount: 15.2.4

exponential approximation

15.3.2 | 15.4

finite time De Vylder approximation

15.6.5

finite time horizon

15.5 | 15.6 | 16.2.2 | 16.3.2

heavy traffic approximation

15.3.8 | 15.4

heavy-light traffic approximation

15.3.10

infinite time horizon

15.1 | 16.2.2 | 16.3.2

ladder heights

15.2 | 20.5.7 | 20.5.8

light traffic approximation

15.3.9 | 15.4

Lundberg approximation

15.3.3 | 15.4

Lundberg inequality

20.5.1 | 20.5.2

Panjer approximation

20.5.8

Renyi approximation

15.3.5 | 15.4

Segerdahl normal approximation

15.6.2

subexponential approximation

15.3.11 | 15.4 | 20.5.7

ultimate

16.1 | 17.1

ruin probability¡`Zero'' approximation

20.5.2

ruin theory

15.1

ruin time

16.1 | 16.2.2 | 17.1

safety loading

16.1 | 20.1 | 20.6.1

relative: 14.2.1 | 15.1 | 15.7

Securities and Exchange Commission

10.4

single-period criterion

20.2

Sklar theorem

2.2.1 | 2.2.3

Skorokhod topology

16.3.1 | 17.2

solvency

20.6

special purpose vehicle (SPV)

4.1

stable distribution

characteristic exponent

density function

1.2.2

direct integration

1.2.2 | 1.4.4

distribution function

1.2.2

FFT-based approach

1.2.2 | 1.4.4

index of stability

maximum likelihood method

1.4.4

method of moments

1.4.3

quantile estimation

1.4.2

regression-type method

1.4.3 | 1.4.3

simulation

1.3

skewness parameter

tail exponent

estimation: 1.4.1

tail index

stochastic process

mean reverting: 7.2

stochastic volatility

7.1 | 8.2.2

calibration: 7.4

strings

5.2 | 5.3

structure variable

14.2.3

Sum of Squared Errors (SSE)

7.4

Support Vector Machine (SVM)

10. | 10. | 10.2

calibration

10.5

cross validation: 10.5 | 10.5

classifier function

10.1

kernel function

Lagrangian formulation

outlier

separating hyperplane

training set

10.1 | 10.3

tail dependence

3. | 3.2

asset and FX returns: 3.6
estimation: 3.4 | 3.5

tail exponent

1.2 | 1.4.1

estimation: 1.4.1
log-log regression: 1.4.1

tail index

3.3.2 | 3.3.2

Takagi-Sugeno approach

11. | 11.3.2

test statistic

Anderson-Darling

1.5 | 4.3 | 13.4.2

Cramér-von Mises

4.3 | 13.4.2

CUSUM

Dickey-Fuller

2.1.3

augmented: 2.1.3 | 11.2.2

half-sample approach

13.4.2

Jarque-Bera