Краткие сведения по стохастической финансовой математике. Барабанов А.Е. - 30 стр.

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π
(x, f
1
) X
π
0
= x X
π
1
= f
1
C
(f
1
) x C
(f
1
)
C
(f
1
) x
x
C
(f
1
)
x π
π = π
= (β
, γ
)
ρ = a X
π
1
=
f
a
= f(S
0
(1 + ρ)) ρ = b X
π
1
= f
b
= f(S
0
(1 + ρ)) X
π
1
= f
1
C
(f
1
) = C
(f
1
) =
1
1 + r
µ
b r
b a
f
a
+
r a
b a
f
b
.
a < r < b
P
P
e
P P
a b
p
=
e
P ({a}) q
=
e
P ({b})
S/B
E
e
P
µ
S
1
B
1
= E
e
P
µ
S
1
B
1
S
0
B
0
= E
e
P
µ
S
0
(1 + ρ)
B
0
(1 + r)
S
0
B
0
=
S
0
(1 + E
e
P
ρ)
B
0
(1 + r)
S
0
B
0
= 0,
E
e
P
ρ = r
N > 1
ρ
n
ρ
n
= a
n
ρ
n
= b
n
n = 1, . . . , N
r
n
a
n
< r
n
< b
n
r
n
a
n
b
n
F
n1
f
N
F
N
a
n
a b
n
b r
n
r
CRR
f
N
N