RMSC 2001
Introduction to Risk Management
Tutorial 8
November 21, 2016
1
Forward and Futures
Definition 1.1. (1) A forward contract is an agreement to buy or sell an asset at a certain
future time for a certain price.
(2) If you assume a long position, yo
RMSC 2001
Introduction to Risk Management
Tutorial 2
CHAN Chu Kin
September 26, 2016
1
Meaning and Classification of Risk
Broadly speaking, risk is defined as uncertainty of having a bad outcome. It has two components:
frequency and severity. To understan
RMSC2001Introduction
IntroductiontotoRisk
RiskManagement
Management
RMSC2001
IV. Financial instruments
Term 1, 2016-17 | Department of Statistics, The Chinese University of Hong Kong
References:
1. Hull, J.C. (2002) Options, Futures and other Derivati
RMSC2001Introduction
IntroductiontotoRisk
RiskManagement
Management
RMSC2001
III. Risk, utility and decisions
Term 1, 2016-17 | Department of Statistics, The Chinese University of Hong Kong
Reference:
Autor, D. (2014) Lecture Note 14: Uncertainty, Exp
RMSC2001Introduction
IntroductiontotoRisk
RiskManagement
Management
RMSC2001
V. Market risk management
Term 1, 2016-17 | Department of Statistics, The Chinese University of Hong Kong
References:
1. Hull, J.C. (2002) Options, Futures and other Derivati
Let me share two other factors about five forces.
Substitute Services
Although there is no substitute product for a necessity
like furniture,there are many substitute services for
providing fuiniture.First,Brand Furniture.Most of them
use simlar methods t
Assignment 9 (HUANG, Huilin 1155028967)
Over the years, our research team conducted data analysis mainly by applying
classical statistical methods. We set lots of assumptions when we analyze data while
sometimes there comes bias since we set too many cond
FINA 3080 Assignment Part 1 & 2 | HUANG, Huilin 1155028967
Part 1: Stock Code: 2318. HK PING AN
Introduction:
Ping An Insurance (Group) Company of China, Ltd (abbreviated to Ping An) is the
first joint-stock insurance company in China providi
STAT 4008
Survival Modeling
Assignment 1 (Solution)
Department of Statistics, The Chinese University of Hong Kong
1
Question 1
Suppose a discrete random variable T taking values 2, 4, 5, 7, 9, 12 with probabilities
respectively.
(a) Find the mean of T .
(
2.1
Likelihood Construction for Censored Data
Likelihood function:
If x1, x2, . . . , xn are the values of a sample from a population with parameter , the likelihood function of the sample
is given by
L() = f (x1, x2, . . . , xn; )
for the values of with
RMSC 2001 Introduction to Risk Management Science (Term 1 2014)
Mid-term Examination Preparation
The exam covers all the materials that have been discussed so far in this course, including
i. Introduction to risk management: Meaning of risk, various types
RMSC 2001 Introduction to Risk Management Science (Term 1 2014)
Mid-term Examination Preparation
The exam covers all the materials that have been discussed so far in this course, including
i. Introduction to risk management: Meaning of risk, various types
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term 1 2014
Mid-term Practice Problems
1. The spreading of losses incurred by a few individuals over a larger group, so that average loss is
substitu
Department of Statistics, The Chinese University of Hong Kong
RMSC 2001 Introduction to Risk Management | Term 1 2014
Final Exam Information Sheet
1. As organised by Registration and Examinations Section, the final examination (the exam) is scheduled on 9
Example of distribution of two continuous random variables
Let the joint p.d.f. of X and Y be
3
f ( x, y ) x 2 (1 | y |), - 1 x 1. - 1 y 1.
2
(a)
(b)
(c)
(d)
What is F(0.5,0.5)=P(X0.5,Y0.5)?
What are the marginal p.d.f. of X and Y?
What is the conditional
Moments and moment generating function are completely new to most of you. Therefore it is
worthwhile to spend more time and use more examples to understand them.
1. Moments:
Firstly, we explained mean, variance, skewness, are important quantities that can
1.1-2 Probability of insuring exactly 1 our. HA) = 0.]
Probability of mnunng more than I eat. H3) = 0.9
Pxobnbilily of insuring a sperm cu. P(C') = 0.25
P(B n C) = 0.10
P(AnC')=P(C)-P(Bn() =0.l = P(A)
PM A 0') = o.
1.1-4 (a) 82 cfw_1111111111. HHHHT. HHHT
STAT2001 Assignment 4
Do all 6 questions. Show your steps clearly.
Deadline for this assignment is 18th Nov. 5:00p.m. You can submit to the assignment locker
(next to LSB 125) or to your Tutors.
Q1. The random variables X and Y have the joint probability
A summary of the special distributions discussed:
For discrete distributions, we have learnt Binomial distribution, Hypergeometric
distribution, Poisson distribution, Geometric distribution, Negative Binomial distribution.
For continuous distributions, we
1. Example 3 on P.13 of chapter 5 notes can also be solved using distribution-function technique:
Y1
X1
, Y2 X 2 ;
X2
f X1 , X 2 ( x1 , x2 ) 2,0 x1 x2 1,
FY1 ,Y2 ( y1 , y 2 )
P (Y1 y1 , Y2 y2 )
P(
X1
y1 , X 2 y2 )
X2
P ( X 1 y1 X 2 , X 2 y2 )
y2 y1x2
5.12 Herew=\/;(7,$=Iand0<w<oomapsont00<y<oo. Thus
2f
g(y)= J37
e y/Q, 0<y<oo.
2ng=
5.1-8 2: = (9W7
1: 3
.17 $03) "(213)
e", 0<z<oo
3/7
W'(%)(%) W
510/7 9 y
a,
A
1.
ll
Q
A
Q
v
II
, 0<y<oo.
5.110 Since-1<z<3.wehavc0$y<9.
When0<y<Lthen
l
xl_. y, _2y-' $2.
Solution for STAT2001 2016 Midterm
1. (a) Let X1 denote the number of babies born during next 5 hours, then
X1 P oisson(1 ), 1 =
5
3 = 0.625
24
So,
P (X1 2) = P (X1 = 0) + P (X1 = 1) + P (X1 = 2)
= e0.625 +
e0.625 0.625 e0.625 0.6252
+
1!
2!
= 0.9743.
(b
1, Applying Expected Value calculation in a decision making problem:
The manager of a bakery knows that the number of chocolate cakes he can sell on any given
day is a random variable with probability mass function
f ( x)
1
6
for x 0,1,2,3,4,5.
He also k
In some settings, random variables can be intuitively considered independent. For example, you roll a
dice twice and let X to be the result of the first throw and Y to be the result of the second throw. In
some modelling exercises, it is also common to as
STAT2001 Tutorial 5 solution
Oct. 18, 2016
Exercise 1
Y B(2000, 0.001)
For n is large and p is small, we could use Poisson distribution to approximate
Binomial distribution. Thus = 2000 0.001 = 2, Y P oisson(2).
P (Y 4) = P (Y = 0) + P (Y = 1) + . + P (Y
STAT2001 Tutorial 4 Solution
Oct. 11, 2016
Exercise 1
(a)
X
P (X = k) = 1
k1
c e2
X e2 2k
k1
c e2
X e2 2k
k!
k0
k!
=1
2 0
e
2
=1
e2
0!
c(e2 1) = 1 c =
e2
1
1
(b)
M (t) = E (exp(tx) = c
X (2et )k
k1
= c
X (2et )k
k!
k0
t
= ce2e
1
X e2et (2et )k
k0
k!
k!
STAT2001 Assignment 5
Deadline for this assignment is 2nd Dec. 5:00p.m. You can submit to the assignment
locker (next to LSB 125), to Blackboard system or to your TAs.
1.
Find the pdf of Y=exp(X) when X follows a normal distribution with mean
and standar
Chapter 5: Distributions of functions of random variables
STAT2001
2016 Term I
Outline
1. Functions of one random variable
2. Transformations of two random variables
3. Several independent random variables
4. Random functions associated with Normal distri
STAT 2001A / 2001B
Basic Concepts in Statistics and Probability I
2016 Term I
1.
Description:
This course is designed to study the basic concepts of probability and statistics. Topics include elementary
probability, Bayes theorem, random variables, distri