... well-educated person
should at least be acquainted with the ideas of calculus, and a scientifically lit-
erate person must know calculus solidly.
Calculus has two main aspects: differential calculus ... possible (in the sense that it gives us ways
to solve these equations).
Calculus Demystified
explains these ideas in a step-by-step and accessible
manner. The author, a renowned t...
... gambling!
This book presents the basic concepts of probability in a simple,
straightforward, easy-to-understand way. It does require, however, a
knowledge of arithmetic (fractions, decimals, and ... books in this
series entitled Pre-Algebra Demystified.
This book can be used to gain a knowledge of the basic concepts of
probability theory, either as a self-study guide or as a supplementary
text...
... Subdifferential calculus for convex functions
Chapter 4.
Subdifferential calculus for convex functions
tvnguyen (University of Science) Convex Optimization 66 / 108
Chapter 4. Subdifferential calculus ... the inf-convolution is exact at x = y
1
+ y
2
and
equality holds.
tvnguyen (University of Science) Convex Optimization 77 / 108
Chapter 4. Subdifferential calculus for convex functions
M...
... Section 23.5 can be readily extended to two-dimensional Brown-
ian motion. Using precisely the same reasoning as in the one-dimensional case, the right-hand
side of equation (23.19) will only be ... E
t
0
f
s
ds
F
t
273
23 Stochastic Calculus
By definition, this must always be true, even if we replace J
t
with J
max
t
on the right-hand side:
J
max
0
≥ E
J
max
t
F
0
+ E...
... independent of
F t
.
The integrand is
t;t 0
,where
1.
t
is
F t
-measurable
8t
(i.e.,
is adapted)
2.
is square-integrable:
IE
T
Z
0
2
t dt 1; 8T:
We want to define the It
ˆ
o Integral:
I ... :
Subtracting one of these from the other and solving for
1
T
, we obtain the “delta-hedging for-
mula”
1
T =
V
2
TH , V
2
TT
S
2
TH , S
2
TT
;
(1.12)
and substitu...