question archive Let τ be the random time when a random walk first hits either the point x = 2 or −2
Let τ be the random time when a random walk first hits either the point x = 2 or −2
Subject:FinancePrice:2.86 Bought7
Let τ be the random time when a random walk first hits either the point x = 2 or −2. That is :
τ = τ1 = min {n : |Sn| = 2}
Please find the probability distribution and the expected value of τ. Hint: You can consider consecutive
pairs with a ’size of 2’ such as (1, 1),(−1, −1) and consecutive pairs such as (−1, 1),(1, −1) separately
and get help from first success probability. (You don’t have to of course, as long as you solve the question
any method is great.)
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
a) Capital Gain = (End price – beginning price) / beginning price
Formula
Capital Gain ($)
Capital Gain Yield
Preferred Stock
(10 – 10) / 10
$0
0 %
Common B
(36.5 -38) / 38
-$1.5
-3.95%
Bond C
(1,035 -985) / 985
$50
5.08%
b) Dividend Yield= Dividend / End price
Formula
%
Preferred Stock
0.75 / 10
7.5 %
Common B
3.35 / 36.5
9.18%
Bond C
78 / 1,035
7.54%
c) Total holding period return
= Dividend + Capital Gain / beginning price
Formula
%
Preferred Stock
(0.75+ 0) / 10
7.5 %
Common B
( 3.35 – 1.5) / 36.5
5.07%
Bond C
(78 + 50) / 985
13%
