absolute risk aversion 1
absolutely continuous measure 1
acceptance set 1, 2, 3, 4, 5, 6, 7
– for conditional risk measure 1
– one-step 1
act 1
adapted process 1
affine hull of a convex set 1
affine numerical representation 1
American claim
– arbitrage-free price of 1, 2
– attainable 1
– hedging strategy 1
American option 1
– call 1
arbitrage bounds 1
arbitrage opportunity 1, 2, 3, 4, 5
arbitrage-free price
– of a contingent claim 1
– of a European claim 1
– of American claim 1
– of an American claim 1
Arrow–Debreu equilibrium 1
– and interest rate 1
– w.r.t. general utility functionals 1
Arrow–Pratt coefficient 1
asymmetric relation 1
at-the-money option 1
atom of a probability space 1, 2, 3
atomless probability space 1, 2
attainable
– American claim 1
– European claim 1
– payoff 1
average
– price option 1
– strike option 1
Average Value at Risk 1
– sensitivity 1
– time-inconsistency 1
backwards martingale 1
Banach space 1
Banach–Alaoglu theorem 1
– Black–Scholes price of 1
– down-and-in put 1
barycenter of a measure 1
Bermuda option 1
Bernoulli, Nicholas 1
Black–Scholes price 1
– of a European call option 1, 2
Bolzano–Weierstraß theorem
– randomized version 1
boundedly supported measures 1
Brownian motion 1
butterfly spread 1
– Asian 1
– Bermuda 1
– universal bounds on price 1
call-put parity 1
cap 1
CARA utility 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
cash additivity 1
– conditional 1
catastrophe bond 1
– functional 1
–multiplicative 1
certainty equivalent 1, 2, 3, 4, 5
– as reservation price 1
– as risk measure 1
– cash-invariant 1
– quasi-convex 1
– relative 1
– translation property 1
certainty independence 1
–weak 1
Choquet boundary 1
coherent conditional risk measure 1
coherent measure of risk 1
– and superhedging 1
coherent monetary utility functional 1
– dynamic 1
– dynamically consistent 1
– representation theorem 1
– time-consistent 1
comonotone random variables 1, 2, 3, 4, 5
comonotonic
– functional 1
– risk measure 1
complete
– relation 1
compound lottery 1
concave function 1
– proper 1
concave monetary utility functional 1
concave stochastic order 1
conditional Average Value at Risk
– time-inconsistency 1
conditional cash invariance 1
conditional coherent risk measure 1
conditional convexity 1
conditional covariance 1
conditional entropic risk measure 1
conditional mean-standard deviation risk measure 1
conditional relative entropy 1
conditional risk measure
– coherent 1
– relevant 1
– representation 1
– sensitive 1
– time consistent 1
Conditional Value at Risk 1
conditional Value at Risk 1
– time-inconsistency 1
– of a convex risk measure 1, 2
connected topological space 1
constant absolute risk aversion 1, 2
constant relative risk aversion 1
contingent claim 1
– American 1
– arbitrage-free price of 1
– attainable 1
– European 1
– redundant 1
– replicable 1
continuation region 1
continuity from above 1, 2, 3, 4
continuity from below 1, 2, 3, 4
convex combination 1
convex function 1
– duality theory 1
– proper 1
convex hull 1
convex measure of risk 1
– law-invariant 1
– penalty function for 1, 2, 3, 4, 5
– relevant 1
– tight 1
– conditional 1
– representation theorem 1
convex set 1
convex stochastic order 1, 2, 3
convexity
– conditional 1
core of a set function 1
cost of superhedging 1
cost process 1
Cox-Ross-Rubinstein model 1, 2, 3
CRRA utility 1
declining a favorable bet 1
Delta of a call option 1
density function 1
derivative 1
Dini’s lemma 1
Dirac measure 1
discount certificate 1
discounted American claim 1
discounted claim 1
distortion function 1
distortion of a probability measure 1
distribution
– normal 1
– Poisson 1
distribution function 1
– and stochastic dominance 1
– and stochastic order 1
– modified 1
divergence risk measure 1
– sensitivity 1
divergence risk measures 1
diversification 1
Doléans–Dade exponential 1
Donsker’s invariance principle 1
Doob’s systems theorem 1
down-and-out option 1
dual space 1
duality theory of convex functions 1
Dunford–Pettis theorem 1
dynamic coherent risk measure 1
dynamic consistency of a risk measure 1
dynamic risk measure
– relevant 1
– sensitive 1
– time consistent 1
–weak time consistency 1
dynamically consistent 1
early exercise premium 1
Eberlein–Šmulian theorem 1
effective domain of a convex function 1
efficient market hypothesis 1
Ellsberg paradox 1
enlagement of filtration 1
entropic risk measure 1, 2, 3, 4
– conditional 1
– sensitivity 1
entropy of a measure 1
entropy-minimizing risk-neutral measure 1, 2
equivalent martingale measure 1, 2
equivalent measure 1
Esscher transform 1
essential infimum 1
– of a random variable 1
essential supremum 1
Euclidean inner product 1
Euclidean norm 1
– efficient hedging of 1
– intrinsic value of 1
– time value of 1
European contingent claim 1
– arbitrage-free price 1
– redundant 1
– replicable 1
European put option 1
exercise strategy for American claim 1
Expected Shortfall 1
expected utility representation 1
expectile 1
expiration date of a contingent claim 1
exponential family 1
exponential utility function 1, 2, 3
extreme point 1
– of comonotonic convex risk measures 1
fair premium 1
fair price 1
–on Lp 1
favorable bet 1
feasible allocation 1
Fenchel–Legendre transform 1, 2, 3, 4, 5, 6
– of a convex risk measure 1, 2
filtered probability space 1
filtration 1
– enlargement of 1
financial position 1
finitely additive set function 1, 2, 3
first-order stochastic dominance 1, 2
fork convex sets 1
forward starting option 1
Fréchet bounds 1
– under portfolio constraints 1
–with contingent initial data 1
function
– concave 1
– convex 1
fundamental theorem of asset pricing
– for multi-period market 1
– geometric form 1
– in one period 1
– under portfolio constraints 1
–with contingent initial data 1
–without a priori measure 1
Gamma of a call option 1
generalized likelihood quotient test 1
generalized trading strategy 1
–mean self-financing 1
geometric Brownian motion 1
Gini coefficient 1
Gini’s mean difference 1
Girsanov formula 1
global quadratic risk 1
Greeks 1
– and Black–Scholes equation 1
– Delta 1
–Gamma 1
– Rho 1
– Theta 1
– Vanna 1
– Vega 1
– Volga 1
–Vomma 1
Hahn–Banach theorem 1
Halmos–Savage theorem 1
Hardy–Littlewood inequality 1, 2
Hausdorff space 1
hedging strategy for American claim 1
Hoeffding–Fréchet bounds 1
hyperbolic absolute risk aversion 1
in-the-money option 1
Inada conditions 1
–on 1
indifference relation 1
inequality
inf-convolution of two risk measures 1
inner product
– Euclidean 1
insider information 1
interest rate 1
inverse function 1
– left-continuous 1
– right-continuous 1
Itô integral 1
Itô’s formula 1
Kolmogorov’s law of large numbers 1, 2, 3
Krein–Šmulian theorem 1
Kunita–Watanabe decomposition 1
λ-efficient allocation 1
L2-admissible strategy 1
least favorable measure 1
– and hypothesis testing 1
Lebesgue decomposition 1
left-continuous inverse 1
Legendre transform 1
lexicographical order 1
likelihood quotient test 1
liquid option 1
local martingale 1
local risk process 1
locally convex space 1
locally risk-minimizing strategy 1
locally riskless bond 1
– change of measure 1
lookback call 1
lookback put 1
– variance of 1
lower quantile function 1
m-stable sets 1
market clearing condition 1
market portfolio 1
Markov property 1
– backwards 1
– convergence theorem 1
– local 1
– of successive densities 1, 2
– reversed 1
– strongly orthogonal 1
– as extension of a pricing rule 1
– minimal 1
martingale representation property 1
maturity of a contingent claim 1
MAXMINVAR 1
MAXVAR 1
mean self-financing strategy 1
mean-preserving spread 1, 2, 3
mean-standard deviation risk measure 1, 2
– conditional 1
mean-variance trade-off process 1, 2
measure
– absolutely continuous 1
– entropy of 1
– equivalent 1
– support of 1
measure of risk
– acceptance set of 1
– cash invariant 1
– comonotonic 1
– continuous from below 1
– convex 1
– monetary 1
– monotone 1
– normalized 1
– penalty function for 1
– positive homogeneous 1
– relevant 1
– representation theorem 1
– subadditive 1
– translation invariant 1
metric space 1
minimal martingale measure 1
Minkowski’s separating hyperplane theorem 1
MINMAXVAR 1
mixture space 1
model uncertainty 1
modified distribution function 1
moment generating function 1
monetary conditional risk measure 1
monetary measure of risk 1
monetary risk measure 1
monetary utility functional
– coherent 1
– concave 1
monotone preference relation
– on assets 1
– on distributions 1
monotone set function 1
negative part 1
negative transitive relation 1
– generalized 1
norm
– Euclidean 1
normal distribution 1, 2, 3, 4
normalized set function 1
– affine 1
– of robust Savage form 1
– of von Neumann–Morgenstern form 1, 2, 3, 4, 5
optimal stopping problem 1
– continuation region 1
– stopping region 1
option 1
– Black–Scholes price 1
optional decomposition 1
– theorem 1
– under constraints 1
optional sampling theorem 1, 2
order dense set 1
orthogonal decomposition
– of a contingent claim 1
out-of-the-money option 1
P&L 1
paradox
– Ellsberg 1
– St. Petersburg 1
partial order 1
pasting of two probability measures 1, 2, 3
– one-step 1
Polish space 1
portfolio 1
portfolio insurance 1
portmanteau theorem 1
positive affine transformations 1
power of a statistical test 1, 2
predictable process 1
predictable representation property 1
predictably convex set 1
preference order 1
preference relation 1
– asymmetry of 1
– continuous 1
– continuous from above 1
– continuous from below 1
– lexicographical 1
– negative transitivity of 1
– numerical representation of 1, 2, 3, 4, 5, 6
– random 1
– risk averse 1
–weak 1
price density 1
price system 1
pricing measure 1
probability measure
– absolutely continuous 1
– equivalent 1
Prohorov’s theorem 1
– for ψ-weak topology 1
proper concave function 1
proper convex function 1
put option 1
– American 1
– Asian 1
– universal bounds on price 1
–with barrier 1
Q-martingale 1
Q-submartingale 1
Q-supermartingale 1
QS-Snell envelope
– upper 1
quadratic risk
– global 1
– local 1
– remaining 1
quantile 1
– and stochastic order 1
– for nonadditive set functions 1
quantile hedging 1
quasi-convexity 1
Radon measure 1
Radon–Nikodym
– derivative 1
– theorem 1
random walk 1
randomized statistical test 1, 2, 3, 4
recursiveness 1
reference portfolio 1
reflection principle 1
regular conditional distribution 1, 2
relation
– antisymmetric 1
– asymmetric 1
– complete 1
– equivalence 1
– indifference 1
– negative transitive 1
– reflexive 1
– conditional 1
relative interior of a convex set 1
relative risk aversion 1
remaining conditional risk 1
replicating
– portfolio 1
– strategy 1
representation theorem for risk measures 1
–on L∞ 1
reservation price 1
return 1
reverse convertible bond 1
reversed martingale 1
Rho of a call option 1
right-continuous inverse 1
risk 1
– absolute 1
– relative 1
risk measure 1
– acceptance set of 1
– cash invariant 1
– comonotonic 1
– dynamic 1
– dynamically consistent 1
– monetary 1
– monotone 1
– normalized 1
– penalty function for 1
– positive homogeneous 1
– representation theorem 1
– subadditive 1
– tight 1
– time-consistent 1
– translation invariant 1
risk neutrality 1
risk premium 1
risk transfer 1
robust representation
– of conditional risk measure 1
robust Savage representation 1, 2, 3
robust shortfall risk 1
second fundamental theorem of asset pricing 1, 2
second-order stochastic dominance 1, 2, 3, 4
self-financing strategy 1
– in continuous time 1
sensitive risk measure 1, 2, 3
separable metric space 1
separating hyperplane theorem 1
separation theorems 1
set
– convex 1
set function
– core of 1
– strongly additive 1
– strongly subadditive 1, 2, 3
Sharpe ratio 1
short sales 1
shortfall 1
– robust 1
significance level of a statistical test 1, 2
simple probability distribution 1
size of a statistical test 1
– lower 1
– upper QS- 1
space of reference portfolios 1
St. Petersburg paradox 1
stability under pasting 1
stable subspace of H 2 1
standard normal distribution 1
statistical test 1
– for composite hypothesis 1, 2
stochastic differential equation 1
stochastic dominance 1
stochastic order
stochastic process 1
– adapted 1
– predictable 1
Stone vector lattice 1
stop-loss contract 1
stopping region 1
stopping time 1
straddle 1
strategy
–L2-admissible 1
– locally risk-minimizing 1
–mean self-financing 1
– self-financing 1
– self-financing in continuous time 1
stress test measures 1
strong law of large numbers 1, 2, 3
strong orthogonality 1
strongly additive set function 1
strongly subadditive set function 1, 2, 3
submartingale 1
– local 1
submodular 1
submodular set function 1, 2, 3
substitution axiom 1
success ratio 1
success set 1
supermartingale 1
– local 1
superreplication strategy 1, 2
support of a measure 1
supremum norm 1
systems theorem 1
theorem
– Doob’s systems theorem 1
– Dunford–Pettis 1
– Eberlein–Šmulian 1
– Hahn–Banach 1
– Halmos–Savage 1
– Krein–Šmulian 1
– optional decomposition 1
– optional sampling 1
– portmanteau 1
– Radon–Nikodym 1
– randomized Bolzano–Weierstraß 1
– separating hyperplane 1
– separation 1
– superhedging duality 1
Theta of a call option 1
tightness
– of a set of measures 1
– of risk measure 1
time consistency 1
–weak 1
time consistency of a risk measure 1
– of a European call option 1
topological space
– connected 1
– Hausdorff 1
topological vector space 1
– locally convex 1
topology
–weak 1
–weak∗ 1
trading strategy 1
–L2-admissible 1
– generalized 1
– replicating 1
– self-financing 1
transitive relation 1
translation invariance 1
translation property 1
– of certainty equivalent 1
type 2 error 1
uncertainty 1
uncertainty aversion 1
underlying 1
uniform Doob decomposition 1
– under constraints 1
universal arbitrage bounds 1, 2
up-and-in call 1
– Black–Scholes price of 1
upper QS-Snell envelope 1
– characterization of 1
upper hedging price 1
upper quantile function 1
– characterization of 1
– optional decomposition of 1
– CARA 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
– CRRA 1
– decreasingly risk averse 1
– exponential 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
utility-based shortfall risk measure 1, 2
Value at Risk 1, 2, 3, 4, 5, 6, 7
– comonotonicity 1
– conditional 1
– time-inconsistency 1
value process 1
Vanna of a call option 1
variance 1
– conditional 1
variance-optimal strategy 1
vector lattice 1
Vega of a call option 1
Volga of a call option 1
Vomma of a call option 1
von Neumann–Morgenstern representation 1, 2, 3, 4, 5
weak certainty independence 1
weak information 1
weak preference order 1
weak time consistency 1
weak topology
– on a Banach space 1
– on a locally convex space 1
weak topology for measures 1
weak∗ topology 1
weakly compact set 1
Wiener measure 1
Wiener process 1
worst conditional expectation 1, 2
worst-case risk measure 1
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