List of Notations
α Decaying factor for MAR
¯x
t
Arithmetic mean of t-th (predict or realized) price relatives
Element-wise product of two vectors
m
Simplex domain
(b;x
t
) -insensitive loss function
Sensitivity parameter for PAMR
γ Proportional transaction cost rate
Integral
R
m
+
Domain of m-dimensional vectors with positive real elements
1 Vector of all 1
b ·x Dot product of vector b and vector x
b
x Dot product of vector b and vector x
b
n
1
A portfolio strategy for n periods
b
t
Portfolio vector for t-th period
I Identity matrix
p
t
Vector of closing prices for t-th period
x
n
1
Whole market windows for n periods
x
e
s
Market windows from period s to e
x
t
Vector of price relatives (simple gross return) for t-th period
N(μ,) Normal distribution with mean μ and covariance matrix
det() Determinant of matrix
EMA
t
(α) Exponential moving average
regret
n
(Alg) Regret of Alg strategy with respect to BCRP
SMA
t
(w) Simple moving average
μ(·) A distribution on the space of valid portfolio
φ Confidence parameter
(·) Cumulative function of normal distribution
ρ Correlation coefficient threshold
˜
x
t+1
Predicted price relative vector
C
t
(w, ρ) Correlation-similar set
i Index of an asset
m The number of assets
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xiv LIST OF NOTATIONS
n The number of trading periods
P Maximum correlation coefficient
S
t
Cumulative return till the end of t-th period
s
t
Daily return for t-th period
S
t
(Alg) Cumulative return achieved by Alg until the end of
t-th period
t Index of a trading period
W Maximum window size
w Window size
W
t
(Alg) Exponential growth rate achieved by Alg until the
t-th period
C Aggressive parameter for PAMR
CORN(w, ρ) Correlation-driven nonparametric expert
CORN-K CORN algorithm with top-K aggregation
CORN-U CORN algorithm with uniform aggregation
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