Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 9.4, Problem 3E
To determine
To find: the floor of the number
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The purpose of this problem is to solve the Black-Scholes PDE with analytical techniques,
which will lead us back to the Black-Scholes formula. The technique is very similar to the
one used with the Feynman-Kac formula back in MATH 467.
Let's consider the PDE given by
with terminal condition f(T,x)
af
+
Ət
1
02
ર
.2მ2 f
af
მ2
+rx
მე
- rf = 0,
=
(x-K)+. The solution f(t, x) corresponds to the price
of a call option (given the initial condition) at time t if the stock price is x.
(a) The first two things that prevent us from solving this PDE directly are
(i) the fact that we have a terminal condition, instead of an initial condition;
(ii) the terms in front of the derivatives are not constant.
To address these, we use the transformation g(t, x) = ƒ(T − t,e³), equivalent to
f(t, x) = g(T-t, log(x)). Under this condition, determine the PDE and the initial
condition satisfied by g.
(b) Now, the PDE obtained in (a) should have an initial condition and constant coeffi-
cients, but it still…
٣:٥٣
النموذج الاول
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O O O
بشما ند الحمر الحمر
الجمهورية الجنية
وزارة التربية والتعليم
اليوم
التاريخ
اللجنة العليا للاختبارات
الزمن
اختبار مادة الجبر والهندسة
لجنة المطابع السرية المركزية
للشهادة الثانوية العامة (القسم العلمي)
الفترة
%97
(1)
ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف ( ص ) للإجابة الصحيحة والحرف ( خ ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي ( درجة لكل فقرة )
)1
)
2
)
3
)
4
) بؤرة القطع س" = ١٢ ص هي (
۲
) طول المحور الأصغر للقطع ٩ س + ص = ٩ يساوي 6 وحدات طول .
) إذا كان & عدد مركب ، 181 + 11 = ٦ ، فإن ١١ = ٣ .
) إذا كان م + ۳ ت = ۲ + ت ب م ، ب دع ، فإن م + ب =
5 ( ) إذا كان & = ۱ + ٣ ت ، فإن ٠ = ١٠ .
6 ( - ) إذا كان ٥٠ - ٣ - ١٢٠ ٤ - ٣ ، فإن قيمة ٧ = ٥ .
1
)
=
N
) إذا كان ح هو الحد الخالي من س في المفكوك ( س +
v. N
8 ( ( قيمة المقدار , = + ۱ ، * . . +
، فإن قيمة ٧ = ١٦ .
۱ +
9 ( ) المستقيمان المقاربان للقطع الذي معادلته س" = ١ هما ص = :
۹
10 ( ) إذا كان ٥ + س = ٢٤ ، فإن قيمة س = - 1
س
11 ( ) إذا كانت النسبة بين الحدين الأوسطين تساوي 9 في المفكوك ( س + - ) ،…
Chapter 9 Solutions
Discrete Mathematics
Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Suppose that you have an unlimited supply of red,...Ch. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.2 - Prove by mathematical induction that n2 − n + 2 is...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prove by mathematical induction that
is a...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 12ECh. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 15ECh. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Consider the sequences of n terms in which each...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.3 - In Exercises 1–24, find an explicit formula for sn...Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 38ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.6 - Prob. 1ECh. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - Prob. 15ECh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - In Exercises 21–26, find constants a and b such...Ch. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Prob. 32ECh. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Prob. 39ECh. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9 - Prob. 1SECh. 9 - Prob. 2SECh. 9 - Prob. 3SECh. 9 - Prob. 4SECh. 9 - Prob. 6SECh. 9 - A data processing position pays a starting salary...Ch. 9 - Prob. 8SECh. 9 - Prob. 9SECh. 9 - Prob. 10SECh. 9 - Prob. 11SECh. 9 - Prob. 12SECh. 9 - Prob. 13SECh. 9 - Prob. 14SECh. 9 - Prob. 17SECh. 9 - Prob. 18SECh. 9 - Prob. 19SECh. 9 - Prob. 21SECh. 9 - Prob. 22SECh. 9 - Prob. 23SECh. 9 - Prob. 41SECh. 9 - Prob. 42SECh. 9 - Prob. 43SECh. 9 - Prob. 44SECh. 9 - Prob. 45SECh. 9 - Prob. 46SECh. 9 - Prob. 47SECh. 9 - Prob. 48SE
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