I INTERNATIONAL SCIENTIFIC CONFERENCE OF YOUNG RESEARCHERS
Baku Engineering University
31
27-28 April 2018, Baku, Azerbaijan
subject to some random environmental effects, so, in this case we will have
"
"
)
(
)
(
noise
t
r
t
a
,
The function
)
(t
r
is assumed to be nonrandom.
2)
Optimal Stopping problem: Suppose a person has an asset or resource (e.g. a house, stocks,
oil...) that he (or she) is planning to sell. The price
)
(t
X
at time t of her asset on the open market
varies according to a stochastic differential equation of the same type as in above :
"
"noise
X
X
a
dt
dX
t
t
t
where
,
a
-are known constants. If the discount rate is a known constant
, then the problem
is at what time should he (or she) decide to sell?
3)
An optimal portfolio problem:
a) a risky investment, where the price
)
(
1
t
q
per unit at time t satisfies stochastic differential
equation
1
1
)
"
"
(
q
noise
a
dt
dq
b) a safe investment,
where the price
)
(
2
t
q
per unit at time t grows exponentially
2
2
q
b
dt
dq
-where
b is
a constant and
a
b
0
will be investigated.
REFERENCE
1.
Feller, W., An Introduction to Probability Theory and Its Applications, Vol. 1, Third edition, Wiley 1968.
2.
Bernt Øksendal Stochastic Differential Equations An Introduction with Applications Fifth Edition, Corrected Printing
Springer-Verlag Heidelberg New York, 1995
3.
Grimmett, G.R. & Stirzaker, D.R., Probability and Random Processes, Second edition, Oxford Science Publications,
1992.
İKİTƏRTİBLİ QEYRİ-XƏTTİ DİFERENSİAL TƏNLİKLƏR SİSTEMİ ÜÇÜN
SƏRHƏD MƏSƏLƏSİNİN SONLU FƏRQLƏR ÜSULU İLƏ HƏLLİ
Lalə DADAŞOVA
Bakı Mühəndislik Universiteti
dadashova.lala@inbox.ru
AZƏRBAYCAN
Aşağıdakı şəkildə qeyri-xətti tənliklər sisteminə baxaq:
1
0
'
,
'
,
,
,
''
'
,
'
,
,
,
''
t
y
x
y
x
t
g
y
y
x
y
x
t
f
x
(1)
Sərhəd şərtlətini aşağıdakı kimi verək
.
1
'
1
'
,
1
1
,
0
'
0
'
,
0
0
1
0
1
0
1
0
1
0
d
y
d
x
d
c
y
c
x
c
b
y
b
x
b
a
y
a
x
a
(2)
(1), (2) məsələsinin aşağıdakı kimi göstərə bilərik:
'
,
,
''
z
z
t
H
z
(3)
2
1
1
'
0
'
1
0
DZ
BZ
CZ
AZ
(4)
Burada
d
b
c
a
g
f
H
y
x
z
y
x
z
2
1
,
,
,
,
