Chapter 3
Life Insurance
Life Table = Mortality table
Notation
lx=number
Basic Relationship
of people alive at age x
dx=number of people die b/w age x and x+1
lx+1=lx-dx
Life/Mortality table
X
lx
dx
0
100,000
2000
1
98,000
1500
2
96,500
1000
3
95,500
900

Chapter 4
Loss distribution
Loss distribution
Life () insurance (Protection against life)
Payment depends on the life time of individuals
Need to know the probability distribution of
death benefits determined
Life time - random
the length of life time
Cas

Chapter 2
Theory of interest
Time value of money
Cash
flow ()
amount of money received (+) or paid out (-) at
some time point
Time
value of money
when valuing cash flows in different time
periods, the interest-earning capacity of money
must taken into a

Chapter One
Introduction
What is Risk ?
What is risk?
This is risk?
This is Risk
The origin of risk can be traced to Latin,
French: risque;
Italian: risco
Meaning cut off like a rock, the sense of peril
to sailors who had to navigate around
dangerous, sha

RMS2001
Introduction to Risk Management
Teachers
Dr.YAU Chun Yip
Email: cyyau@sta.cuhk.edu.hk
Website: www.sta.cuhk.edu.hk/cyyau
Instructor:
Course materials are downloaded here
Office:
Lady Shaw 110
Tutor:
Ms. Wang Weiyin
Email: s1007610491 @sta.c

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RMSC 2001 Exercise 2 Answer
1.
(a)
(b)
2.
(a)
(b)
(c)
(d)
(e)
The dollar you invest at time 1 = (10/1.2)*0.8*(0.9^0.5) = 6.324
The dollar will have accumulated by time 7 = 100/0.8/(0.9^0.5)*1.2 = 142.3
The accumulated value = 500 * (1+0.05/12)^(2*12) = 55

RMS 2001
Exercise 6
1. Suppose your company is involved in a margin buying of 20000 shares of a stock of value
$ 40 per share. 90 % of the total value is borrowed from the bank while the rest are
investment from your company. The maintenance margin requir

RMS 2001
Exercise 4
1. Given the extra life time of a 80-year-old follows uniform distribution
[0, 10]. Find
2 p80 .
q85 .
3 p84 q87 .
2. A 3-year life annuity on a 30-year-old provides for annuity benets of 1
at time 0, 2 at time 1 and 4 at time 2. Yo

RMS 2001
Exercise 7
1. What is the price of a 10-year zero coupon bond with face value 10000 when
the interest rate is 3%?
2. What is the price of a 5-year 6% coupon rate bond with face value 20000
when the interest rate is 2%? (Assuming coupon is also pa

RMS 2001
Exercise 5
1. Suppose the spot price (current stock price) be 98. The below are some
European options that you nd in the market:
Option Number
1
2
3
4
5
Type
Call
Put
Put
Call
Call
Strike price
100
100
95
105
95
option price Maturity
3
3 months
4

Question 1
(a)
Probability Model
CL = 2=1 bi CEi (1 fi )
i
= bN K CEN K (1 fN K ) + bP CEP (1 fP )
where bN K Bernourlli(pN K = 0.1), CEN K = 2 1000 = 2000, fN K = 0.2, bP
Bernourlli(pP = 0.08), CEP = 3 500 = 1500, fP = 0.3.
(b)
E (CL) = pN K CEN K (1 fN

RMS 2001
Exercise 8
1. The below is the history of Stock A. You are holding 1000 shares of stock A.
Day
1
2
3
4
5
6
7
8
Stock price
40
40.3
39.8
38.2
39.5
37.3
37.3
41.1
(a) Find the volatility of Stock A.
(b) Using normal approximation, nd the ve days 1%

RMS 2001
Exercise 9
1. Your portfolio consists of two bonds: two units of North Korean(N.K.) government bonds and three units of Philippines(P.) government bonds. The face
values, the recovery rate and the probability of default for the two bonds are
resp

Chapter 6
Introduction to Market Risk Management
Financial Risk Management
Market Risk
Credit Risk
Borrower does not make payment as promised
Operational Risk
The risk of change in value of the investment/trading
portfolio
Risk arising from people/systems

Chapter 7
Introduction to Credit Risk Management
Financial Risk Management
Market Risk
Credit Risk
borrower does not make payment as promised
Operational Risk
The risk of change in value of the investment/trading
portfolio
Risk arising from people/systems

Chapter 5
Introduction to Financial instruments
5.1 Introduction
Securities () = all financial instruments
Assets/ Equities ()
Commodities ()
Stocks() ownership of the firm
e.g. oil, gold, silver
Debts ()
Bonds() lend money to the firm
5.1 Introduction
Fi

RMSC 2001 Introduction to Risk Management
Tutorial 3 (2012/13)1
February 4/5, 2013
Outline:
1. Certainty Equivalent
2. Coecient of Absolute Risk Aversion
=
1. Certainty Equivalent
The guaranteed amount of money that an individual would view as equally des

Chapter 3b
Insurance
Outline
1.
2.
Introduction
Life Insurance and Life Annuity
a)
b)
3.
4.
Life Table
Calculating fair premium
Moral Hazard
Adverse Selection
1. Introduction
Insurance is the pooling of unexpected
losses by transfer of such risk to insure

1
CHAPTER 2
Decision making under risk
2
Chapter Outline
Expected Value Rule
2. Expected Utility Rule
1.
1.
2.
3.
St. Petersberg Paradox
Expected Utility Rule
Some worked examples
Utility functions
3.
1.
2.
3.
Important characteristics of utility function

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RMSC2001: Introduction to Risk Manag_ernent
hours
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RMSC2001: Introduction to Risk
Management
Lecturer: Dr. John Wright
TA: Chan Kin Wai
Previously
We looked at different types of life insurance
Whole, term, VL, UL etc.
We found that by equating the expected PVs of p
ayments from the insurer and the ins

RMSC2001: Introduction to Risk
Management
Lecturer: Dr. John Wright
TA: Chan Kin Wai
Previously
We introduced , the time of death, as the key rand
om variable
Through the distribution of , we could calculate th
e expectation and variance of the PV of be