exercise, it is verified that the up-and-out call price v(t, x) given by (7.3.20) satisfies the boundary condition (7.3.6). Furthermore, the limit as x↓0 sat- isfies (7.3.5) and the limit as t↑ T satisfies (7.3.7). (i) Verify by direct substitution into (7.3.20) that (7.3.6) is satisfied. (ii) Show that, for any positive constant c, lim 8+ (7, 1-2) = =-∞, lim 8+ (7, -2) = 10 =∞. (7.8.11) Use this to show that for any p = R and positive constants c₁ and c2, we have lim x² NT, [N (81 (T )) x ― NT, C2 ())] = 0, (7.8.12) (7.8.13) *10 lima [N (64 (,))-N (64 (T, 27))] = 0. 10 If p≥0, (7.8.12) and (7.8.13) are immediate consequences of (7.8.11). However, if p< 0, one should first use L'Hôpital's rule and then show that T, lim 2º exp { - 1½ 61 (1,²±² ) } = 0, lim ³ exp{}()} = 0. (7.8.14) To establish (7.8.14), you may wish to prove and use the inequality 1 ༨༨ 1 ža² − b² ≤ (a + b)² for all a, b € R. (7.8.15) Conclude that lim×40 v(t, x) = 0 for 0 ≤t 1. - Use this to show that lim-40 v(t, x) = (x − K)+ for 0 < x < B.
exercise, it is verified that the up-and-out call price v(t, x) given by (7.3.20) satisfies the boundary condition (7.3.6). Furthermore, the limit as x↓0 sat- isfies (7.3.5) and the limit as t↑ T satisfies (7.3.7). (i) Verify by direct substitution into (7.3.20) that (7.3.6) is satisfied. (ii) Show that, for any positive constant c, lim 8+ (7, 1-2) = =-∞, lim 8+ (7, -2) = 10 =∞. (7.8.11) Use this to show that for any p = R and positive constants c₁ and c2, we have lim x² NT, [N (81 (T )) x ― NT, C2 ())] = 0, (7.8.12) (7.8.13) *10 lima [N (64 (,))-N (64 (T, 27))] = 0. 10 If p≥0, (7.8.12) and (7.8.13) are immediate consequences of (7.8.11). However, if p< 0, one should first use L'Hôpital's rule and then show that T, lim 2º exp { - 1½ 61 (1,²±² ) } = 0, lim ³ exp{}()} = 0. (7.8.14) To establish (7.8.14), you may wish to prove and use the inequality 1 ༨༨ 1 ža² − b² ≤ (a + b)² for all a, b € R. (7.8.15) Conclude that lim×40 v(t, x) = 0 for 0 ≤t 1. - Use this to show that lim-40 v(t, x) = (x − K)+ for 0 < x < B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
plz see the picture and solve it. (step by step plz)
![exercise, it is verified that the up-and-out call price v(t, x) given by (7.3.20)
satisfies the boundary condition (7.3.6). Furthermore, the limit as x↓0 sat-
isfies (7.3.5) and the limit as t↑ T satisfies (7.3.7).
(i) Verify by direct substitution into (7.3.20) that (7.3.6) is satisfied.
(ii) Show that, for any positive constant c,
lim 8+ (7, 1-2) = =-∞, lim 8+ (7, -2) =
10
=∞.
(7.8.11)
Use this to show that for any p = R and positive constants c₁ and c2, we
have
lim x² NT,
[N (81 (T ))
x
―
NT,
C2
())]
= 0,
(7.8.12)
(7.8.13)
*10
lima [N (64 (,))-N (64 (T, 27))] = 0.
10
If p≥0, (7.8.12) and (7.8.13) are immediate consequences of (7.8.11).
However, if p< 0, one should first use L'Hôpital's rule and then show
that
T,
lim 2º exp { - 1½ 61 (1,²±² ) } = 0, lim ³ exp{}()}
= 0.
(7.8.14)
To establish (7.8.14), you may wish to prove and use the inequality
1
༨༨
1
ža² − b² ≤ (a + b)² for all a, b € R.
(7.8.15)
Conclude that lim×40 v(t, x) = 0 for 0 ≤t<T.
(iii) Show that, for any positive c,
-∞
lim (7, c) =
0
if 0<c< 1,
if c = 1,
(7.8.16)
T10
80
if c> 1.
-
Use this to show that lim-40 v(t, x) = (x − K)+ for 0 < x < B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c680976-d041-43f6-b2b7-59630778639d%2Fb4286a3c-df38-4c5f-9e7c-3c30d0ff70f9%2Fmde8t5p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:exercise, it is verified that the up-and-out call price v(t, x) given by (7.3.20)
satisfies the boundary condition (7.3.6). Furthermore, the limit as x↓0 sat-
isfies (7.3.5) and the limit as t↑ T satisfies (7.3.7).
(i) Verify by direct substitution into (7.3.20) that (7.3.6) is satisfied.
(ii) Show that, for any positive constant c,
lim 8+ (7, 1-2) = =-∞, lim 8+ (7, -2) =
10
=∞.
(7.8.11)
Use this to show that for any p = R and positive constants c₁ and c2, we
have
lim x² NT,
[N (81 (T ))
x
―
NT,
C2
())]
= 0,
(7.8.12)
(7.8.13)
*10
lima [N (64 (,))-N (64 (T, 27))] = 0.
10
If p≥0, (7.8.12) and (7.8.13) are immediate consequences of (7.8.11).
However, if p< 0, one should first use L'Hôpital's rule and then show
that
T,
lim 2º exp { - 1½ 61 (1,²±² ) } = 0, lim ³ exp{}()}
= 0.
(7.8.14)
To establish (7.8.14), you may wish to prove and use the inequality
1
༨༨
1
ža² − b² ≤ (a + b)² for all a, b € R.
(7.8.15)
Conclude that lim×40 v(t, x) = 0 for 0 ≤t<T.
(iii) Show that, for any positive c,
-∞
lim (7, c) =
0
if 0<c< 1,
if c = 1,
(7.8.16)
T10
80
if c> 1.
-
Use this to show that lim-40 v(t, x) = (x − K)+ for 0 < x < B.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
