MA503a
(FALL 2009)
HOMEWORK #2 Due Wednesday, September 23, 2009
2 1) Recall that the Variance of a random variable X is dened by X := E [X E (X )]2 . Show that 2 (i) X = E [X 2 ] (E [X ])2 ; 2 (ii) X = E cfw_X (X 1) + X 2 , where X = E [X ]. X
Argue that
Unit 2, My MC's Solution
Module 1( Electrostatics, Electricity and Electromagnetism)
Q#
1
2
3
4
Key
D
A
C
B
5
6
7
8
B
A
A
C
9
10
D
A
11
12
D
B
13
A
14
15
C
B
Explanations
E= V/d = 12/(0.15) = 8 V/m
In dark PD across LDR = 50/(50+10) x 12 =10V
Recall
Redra
CAPE PHYSICS MULTIPLE CHOICE
UNIT 2
MODULE 1
ELECTROSTATICS, ELECTRICITY, ELECTORMAGNETISM
(1) A pair of parallel plates has a potential difference of 12V across them and is
15cm apart. What is the electric field strength between the plates?
[A] 0.8V/m
[B
LANGUAGE TECHNIQUES &
STRATEGIES
PURPOSE
TYPE OF DISCOURSE
Narration (tells a story, details a series of
related events)
To entertain, to inform
Novels, biographies, short stories and
autobiographies
Narration
I took her hand in mine, and we went out
Anaconda caught
By SASHA HARRINANAN Monday, December 31 2012
SHE'S SO ROYAL: This majestic 16-foot anaconda, found on a private road in Caroni yesterday afternoon by two
security guards, is seen last night. The .
A BEAUTIFUL 200-pound, 16-foot-long anacon
MATH-503
Homework-3
Solution
Note: In this solution, a strategy h = (x, y1 , , yn ), where x is the riskless asset, yi is the number of shares of the risky asset. 1) a) i. . If 1 + R > u, consider the strategy h = (S0 , 1). Clearly, V0h = 0, and V1h = S0
MA503a
(FALL 2009)
HOMEWORK #3 Due Wednesday, October 7, 2008
B 1) Let cfw_Bt : t 0 be a Brownian motion, and cfw_Ft t0 be the ltration generated by B . Dene 2 B Mt = Bt t, t 0. Show that M is an cfw_Ft -martingale.
2) Let X = cfw_Xn be a martingale with
MA503a
(Fall 2009)
HOMEWORK #4 Due Friday, October 30, 2009
1) Suppose that cfw_ t : t 0 is a standard Brownian motion. Show that for any constant c > 0, the scaled B process Wt := cBt/c , t 0 is also a standard Brownian motion. 2) Let cfw_Bt : t 0 be a s
MA503a
HOMEWORK #5
(Fall 2009)
Due Friday, November 20, 2009
1) Exercise 6.1 (of Bjrks book). o 2) Consider a market that has one bond and one stock, with the following price dynamics: dB (t) = B (t)r(t)dt; dS (t) = S (t)[(t)dt + (t)dW (t)]. Let h(t) = (x
MATH503b/506
(SPRING 2010)
FINAL PROJECT Due Friday, May 7, 2010
1) Consider a bond markdet in which the short rate is modeled by the SDE: dr(t) = (t, r(t)dt + (t, r(t)dW (t), where W is a Brownian motion under the objective measure P . a) Explain how a m
MATH503b
(SPRING 2010)
HOMEWORK #1 Due Friday, January 29
1) Exercise 8.1, 8.2, 8.3 and Exercise 9.2, 9.5, 9.10, 9.11 (of Bjrks book). o 2) Let p(t, s) = C (t, s, K, r, , T ) be the price function of the European call option. Namely p(t, s) = sN (d1 (t, s
MATH503b
(SPRING 2010)
HOMEWORK #2 Due Wednesday, February 17
1) Let H be a complex inner product space, whose inner product is dened by (x, y ) = xy , for all x, y H. Let x := (x, x)1/2 . Prove the Cauchy-Schwartz inequality: |(x, y )| x y , x, y H.
Usin
MATH503b
(SPRING 2010)
HOMEWORK #3 Due Wednesday, March 10, 2010
1) Exercise 11.1 (of Bjrks book). o 2) Exercise 15.3, 15.4, and 15.5 (of Bjrks book). o 3) Consider a market containing one bond and two stocks, and is described by the following SDEs: dB (t
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