The Hong Kong Polytechnic University
AMA 273
Syllabus
Semester Two 2009/2010
Course Instructor:
James Huang (Office: HJ 616, Tel: 2766 6961, email: majhuang@inet.polyu.edu.hk)
Office Hour: Monday 2:00-4:00 pm, Friday 2:00-4:00 pm
Learning Outcomes
The lea

BSc (Hons) in Investment Science (63023)
AMA372: Mathematical Methods for Risk Management
Lecture Notes Part I
Prepared by Dr. Joseph Lee
Probability - axiomatic approach :
In the above experiment of the tossing of a coin
twice, the event of having exactl

BSc (Hons) in Investment Science (63023)
AMA372: Mathematical Methods for Risk Management
Lecture Notes Part III
Prepared by Dr. Joseph Lee
We recall the case that if X N (0, 12), then
1
X 2 ( 1 , 2 ). What about other general ran2
Example
Suppose X U [0,

BSc(Hons) in Investment Science (63023)
AMA372: Mathematical Methods for Risk Management
Lecture Notes Part IV
Prepared by Dr. Joseph Lee
Individual Risk Models for a short term
Suppose the probability of a claim during the
year is denoted by q . Thus, th

Department of Applied Mathematics
The Hong Kong Polytechnic University
AMA372 Mathematical Methods for Risk Management
Assignment 1.
May I remind students that solutions with detailed workings presented in a clear, decent, formal,
precise and concise math

Department of Applied Mathematics
The Hong Kong Polytechnic University
AMA372 Mathematical Methods for Risk Management
Assignment 2.
Question 1.
Consider the random experiment of tossing a coin twice, = cfw_ HH, HT, T H, T T . Suppose we
assign probabilit

Department of Applied Mathematics
The Hong Kong Polytechnic University
AMA372 Mathematical Methods for Risk Management
Assignment 3.
Question 1.
We recall that
(t) =
0
xt1 ex dx
for t > 0.
(a) Show that
(t) = 21t
12
y 2t1 e 2 y dy.
0
Thus, conclude that

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Department of Applied Mathematics
The Hong Kong Polytechnic University
AMA372 Mathematical Methods for Risk Management
Assignment 4.
Question 1. Suppose X and Y are independent random variables with densities
fX (x) = 2 I [0, 1 ] (x) and fY (y ) =
2
1
I (

AMA 273, Lecture 3
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 3
Outline of Lecture 3
Chapter 8: Introduction to Optimization.
Chapter 9: The Derivative in Economics (I).
James Huang
AMA 273, Lecture 3
Chapter 8: Introduction to Optimization.

AMA 273, Lecture 2
James Huang
January 17, 2010
James Huang
AMA 273, Lecture 2
Outline of Lecture 2
Chapter 4: The Elements of Finance.
Supplementary Topics: Present Value Analysis.
James Huang
AMA 273, Lecture 2
Simple Interest Rate
Simple Interest Rate:

AMA 273, Lecture 13
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 13
Outline of Lecture 13
Introduction to Option.
Stock Price Dynamics: Geometric Brownian Motion (GBM)
Models.
Option Pricing: Black-Scholes (BS) Formula and PDE.
Term Structure

AMA 273, Lecture 1
James Huang
January 7, 2010
James Huang
AMA 273, Lecture 1
Outline of Lecture 1
Chapter 1: Mathematical Models in Economics.
Chapter 2: Mathematical Terms and Notations.
Chapter 3: Sequences, Recurrences, Limits.
James Huang
AMA 273, Le

AMA 273, Lecture 4
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 4
Outline of Lecture 4
Chapter 10: The Derivative in Economics (II).
Section 10.1: The Ecient Small Firm
Section 10.2: Startup and Breakeven Points
Worked Examples
James Huang
AMA

AMA 273, Lecture 5
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 5
Outline of Lecture 5
Chapter 11: Partial Derivatives.
Chapter 12: Applications of Partial Derivatives.
James Huang
AMA 273, Lecture 5
Chapter 11: Partial Derivatives.
Section 11

AMA 273, Lecture 6
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 6
Outline of Lecture 6
Chapter 13: Optimization In Two Variables.
Chapter 14: Vectors, Preferences and Convexity.
James Huang
AMA 273, Lecture 6
Chapter 13: Optimization In Two Va

AMA 273, Lecture 7
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 7
Outline of Lecture 7
Chapter 21: Constrained Optimization.
Section 21.1 The Elementary Theory of the Firm.
Section 21.2 The Method of Lagrange Multipliers.
Section 21.3 The Cost

AMA 273, Lecture 8
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 8
Outline of Lecture 8
Chapter 22: Lagrangeans and the Consumer.
Section 22.1 Lagrangeans: A More General Formulation.
Section 22.2 The Elementary Theory of the Consumers.
Section

AMA 273, Lecture 9
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 9
Outline of Lecture 9
Textbook 2, Chapter 5: Multiple Integrals.
Section 5.1 Double Integrals
James Huang
AMA 273, Lecture 9
Two Variable Function
Consider a real valued function

AMA 273, Lecture 10
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 10
Outline of Lecture 10
Textbook 1, Chapter 27: First-order Dierential Equations.
Textbook 2, Chapter 7.2: First-order Dierential Equations.
James Huang
AMA 273, Lecture 10
Chap

AMA 273, Lecture 11
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 11
Outline of Lecture 11
Textbook 1, Chapter 28: Second-order Dierential Equations.
James Huang
AMA 273, Lecture 11
Chapter 28: Second-order Dierential Equations.
Consider a cont

AMA 273, Lecture 12
James Huang
January 8, 2010
James Huang
AMA 273, Lecture 12
Outline of Lecture 12
Solow Growth Model
Textbook 2, Chapter 9: Partial Dierential Equation.
James Huang
AMA 273, Lecture 12
Solow Growth Model
The Solow growth model is intro

BSc (Hons) in Investment Science (63023)
AMA372: Mathematical Methods for Risk Management
Theorem
If X has a discrete uniform distribution, then
Lecture Notes Part II
Prepared by Dr. Joseph Lee
Denition Each member of the family of dis-
2
+1
E [X ] = N2 ,