IEOR 4102, HMWK 3, Professor Sigman
1. A stock has an initial price of S0 = 40. Sn denotes the price at time n, where we assume
the binomial lattice model with parameters
u = 1.25
d = 1.01
p = 0.55.
(a) Compute E(S1 ) and E(S2 ).
SOLUTION: Note that E(Y )

IEOR 4102, HMWK 1, Professor Sigman
1. An asset price starts off initially at price $7.00 at the end of a day (day 0), and at
the end of each consecutive day, independent of the past, the price goes up by one
dollar (with probability p = 0.6) or down by o

IEOR 4102, HMWK 2 Solutions, Professor Sigman
1. Consider the Rat in the Open Maze; 4 rooms, and the outside (state 0), but now the
probabilities are different whenever the rat leaves room 3: P3,1 = 1/8, P3,4 = 7/8;
all the other probabilities are equally

c 2016 by Karl Sigman
Copyright
1
Gamblers Ruin Problem
Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial
fortune of $i and then on each successive gamble either wins $1 or loses $1 independent of the
past with probabil

c 2016 by Karl Sigman
Copyright
1
Stopping Times
1.1
Stopping Times: Definition
Given a stochastic process X = cfw_Xn : n 0, a random time is a discrete random variable
on the same probability space as X, taking values in the time set N = cfw_0, 1, 2, .