ACST601
Stochastic Methods In
Finance and Insurance
Lecture 1
ACST601 2014
1
1. Experiments and Probability
Experiments; Sample Spaces and Events
Probability
Rules of Probability
Venn Diagrams
Permutations and Combinations
Relative Frequency and Probabili

DEPARTMENT OF
MATHEMATICS
NAME: Lai Ruohan
ACST604 S114
Student Id: 42675138
Mathematical Modelling
Assignment 5
FACULTY OF SCIENCE
Due 3 pm 05/06 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Please hand th

DEPARTMENT OF
MATHEMATICS
NAME: Lai Ruohan
ACST604 S114
Student Id: 42675138
Mathematical Modelling
Assignment 6
FACULTY OF SCIENCE
Due 3 pm 12/06 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Please hand th

ACST604 S114
Mathematical Modelling
FACULTY OF SCIENCE
Lai Ruohan
42675138
Group
Assignment 1
Due at 3 pm on 20 March, 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Your assignment
should be handed in at the

DEPARTMENT OF
MATHEMATICS
NAME: Lai Ruohan
ACST604 S114
Student Id: 42675138
Mathematical Modelling
Assignment 4
FACULTY OF SCIENCE
Due 3 pm 15/05 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Please hand th

ACST604 S1 2014: Mathematical Modelling Assignment 4 solutions
Algebra
1. (a) What is an elementary matrix?
(b) Explain why every elementary matrix has an inverse, which is also an elementary matrix.
(c) Give an example of a 3 by 5 matrix, with no 0 entri

DEPARTMENT OF
MATHEMATICS
NAME: Lai Ruohan
ACST604 S114
Student Id: 42675138
Mathematical Modelling
Assignment 2
FACULTY OF SCIENCE
Due 3 pm 10/04 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Please hand th

ACST604 S1 2014: Mathematical Modelling Assignment 2 solutions
Algebra
1. Consider the points shown below in R2 . By means of the diagram, not by solving equations, estimate
values for s and t so that z = sx + ty.
z
x
y
2. Find vectors v and w such that v

ACST604 S1 2014: Mathematical Modelling Assignment 1 solutions
Calculus
1. Inverse function:
(a) Explain why the function y = x2 does not have an inverse function.
(b) Explain the relation between the graphs of function f and its inverse f 1 (x) .
x+2
(c)

Question
7:
You arrange the 30 year loan as in question 6. Immediately after
you get the loan, there is a change in your financial
circumstances, and you are able to increase the monthly
repayment by 100% (so you pay double the required monthly
repayment

Question
5:
You want to borrow to buy a home. You earn $96,000 per year
before tax and the bank will only let you borrow an amount
that requires 25% of your before tax income in monthly
repayments. If the loan term is 20 years, and the repayments
are mont

c. Suppose that the markup decreases to 40%. What will happen to the natural rate
of unemployment? Explain what may cause the markup to decrease.
If m decreases then m/p increases.
For example,(1-u)2*0.8=1/(1+0.4), u=5.51%
An decrease in the relative pric

Question
2:
Compute the coupon payment per period and coupon rate per
year on a bond that has:A price of $98.00, a face value of $100,
a yield to maturity of 6% p.a. convertible quarterly, and a term
of 6 years. Assume the coupon interest income is payabl

Question
3:
Compute the term to maturity of a bond with A price of $96.00,
a face value of $100, a yield to maturity of 7% p.a. convertible
half yearly, and a coupon rate of 5% p.a. convertible half yearly.
Is the term equal to 2 years? If not, what coupo

DEPARTMENT OF
MATHEMATICS
NAME: Lai Ruohan
ACST604 S114
Student Id: 42675138
Mathematical Modelling
Assignment 3
FACULTY OF SCIENCE
Due 3 pm 01/05 2014
Please sign the declaration below, and staple this sheet to the front of your solutions. Please hand th

Question 1 [3 marks]
How many 4-digit numbers can be formed with the 10 digits 0, 1, 2, . . . , 9 (leading zero is not
permitted) if
a. repetitions are allowed,
b. repetitions are not allowed,
c. the last digit must be zero and repetitions are not allowed

ACST601: Homework Exercises - Week 1
1.
D
blue
A
red
B
yellow
C
0
5
10
15
20
E
F
G
H
grey
maroon
pink
olive
1
6
11
16
21
2
7
12
17
22
3
8
13
18
23
4
9
14
19
24
lime
A game of Rollette is played where a Chocolate wheel is spun and the
outcome of interest i

ACST604 VIDEO - Due 5:00 pm 30/5/2014
Introduction
The aim of this exercise is to get creative and communicate something about how mathematical modelling can
provide signicant insight into a problem of economic or nancial interest by producing a vodcast.

MATRKES
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TAYLOR EXPANSION
DEFINITION
Let f(x) be a non-linear function with derivatives up
is
to the nth order. We denote f(x) the first derivative
of f with respect to x and by f(x),f(x),f(n)(x) the
second, third and higher order derivatives of f,
assumning thes

Taylor Series in the
Derivation of Its Lemma
http:/www.youtube.com/watch?v=y4VFtCStgFI
Its Lemma can be regarded as a natural extension of other, simpler
results. Consider a continuous and differentiable function G of a variable
x. If x is a small change

PROJECTS FOR CHAPTER NINE
533
PROJECTS FOR CHAPTER NINE
1. Medical Case Study: Drug Desensitization Schedule11
Some patients have allergic reactions to critical medications for which there are no effective alternatives. In some such cases, the drug can be

7. ODINARY DIFFERENTIAL
EQUATIONS
7.1. Introduction
A differential equation is one that involves one or more derivatives. With an
ordinary differential equation (ODE for short) there are two variables, usually a and y and the
dy d2y
derivatives will be dx