Financial Risk
Andrey Mudrov
Department of Mathematics, University of Leicester,
University Road, LE1 7RH Leicester, UK
am405@le.ac.uk
References
[1] Stephen G. Kellison: Theory of Interest, 2008.
[2] P. Artzner, F. Delbaen, J.-M. Eber, D.Heath: Denition
MA7674
No. of Pages:
No. of Questions:
APRIL EXAMINATIONS
5
6
Subject
ACTUARIAL SCIENCE
Title of paper
MA7674 ACTUARIAL MATHEMATICS
Time allowed
Three hours
Instructions to candidates
This paper contains 6 questions.
Full marks may be obtained from correc
MA7674
No. of Pages:
No. of Questions:
SEPTEMBER EXAMINATIONS
5
6
Subject
ACTUARIAL SCIENCE
Title of paper
MA7674 ACTUARIAL MATHEMATICS
Time allowed
Three hours
Instructions to candidates
This paper contains 6 questions.
Full marks may be obtained from co
MA7674
No. of Pages:
No. of Questions:
APRIL EXAMINATIONS
5
6
Subject
ACTUARIAL SCIENCE
Title of paper
MA7674 ACTUARIAL MATHEMATICS
Time allowed
Three hours
Instructions to candidates
This paper contains 6 questions.
Full marks may be obtained from correc
Faculty of Actuaries
Institute of Actuaries
EXAMINATION
13 April 2005 (am)
Subject CT4 (103)
Models (103 Part)
Core Technical
Time allowed: One and a half hours
INSTRUCTIONS TO THE CANDIDATE
1.
Enter all the candidate and examination details as requested
MA7404
a module for the MSc/PGDip in Actuarial Science
Models in Actuarial Mathematics
Module MA7404
Models in Actuarial Mathematics
Edition 1, September 2011
c University of Leicester 2011
All rights reserved. No part of the publication may be reproduced
MA7404
Coursework Questions
1
Chapter 1
Principles of actuarial modelling
H1.1. [5 marks]
(Institute of Actuaries Examination, CT4(103), September 2005)
An insurance company has a block of in-force business under which policyholders have been given option
MA7404
No. of Pages:
No. of Questions:
PROJECT
Subject
ACTUARIAL SCIENCE
Title of paper
MA7404 MODELS
Time allowed
1
1
Deadline: end of semester
Instructions to candidates
This project represents 30% of the module assessment.
You are required to write a r
MA7406
a module for the MSc/PGDip in Actuarial Science
Further Statistics
Module MA7406
Further Statistics
Edition 1, January 2012
c University of Leicester 2012
All rights reserved. No part of the publication may be reproduced, stored in
a retrieval syst
Chapter 3
Time series analysis
In previous modules you have studied the mathematics of stochastic models,
and in later chapters we will consider particular applications of the techniques
within the nancial world. However, before we do that it is useful to
Chapter 2
Credibility theory
In this chapter we consider credibility theory and the Bayesian approach to
credibility theory. We rst introduce the credibility premium formula and
credibility factor, then explain Bayesian credibility and empirical Bayesian
MA7406
No. of Pages:
No. of Questions:
Course Project
Subject
ACTUARIAL SCIENCE
Title of paper
MA7406 FURTHER STATISTICS
Time allowed
2
1
Deadline: 4pm, Friday the 11th May, 2012
Instructions to candidates
This project represents 30% of the module assessm
Financial Risk
Andrey Mudrov
Department of Mathematics, University of Leicester,
University Road, LE1 7RH Leicester, UK
am405@le.ac.uk
Lecture 7 (Risk Measures)
There are two characteristics attributed to nancial risk that make it measurable and mathemati
Financial Risk
Andrey Mudrov
Department of Mathematics, University of Leicester,
University Road, LE1 7RH Leicester, UK
am405@le.ac.uk
Lecture 4, Duration and Convexity Adjustment
Duration is an important characteristic of cash ow. It is a measure of how
U.U.D.M. Project Report 2009:7
Pricing Asian Options using Monte Carlo
Methods
Hongbin Zhang
Examensarbete i matematik, 30 hp
Handledare och examinator: Johan Tysk
Juni 2009
Department of Mathematics
Uppsala University
Acknowledgements
First of all, I her
THE PRICING OF ASIAN
OPTIONS
Abubakar Addae1
14th September 2006
ABSTRACT
Asian options are a variety of so-called exotic financial derivatives, where the contract
specifies a future payoff depending on the average of a stock price or index over a specifi
Pricing Asian Options with Stochastic
Volatility
Jean-Pierre Fouque and Chuan-Hsiang Han
June 5, 2003
Abstract
In this paper, we generalize the recently developed dimension reduction technique of Vecer for pricing arithmetic average Asian options. The ass
New pricing of Asian Options
Jan Vee
cr
Visiting Assistant Professor of Financial Engineering,
Department of Industrial and Operations Engineering, University of Michigan.
Visiting Associate Professor, Institute of Economic Research, Kyoto University, Jap
Financial Mathematics II
R AY K AWAI1
1 This
Version: November 3, 2011. Email Address: reiichiro.kawai@le.ac.uk. Postal Address: Department of Mathematics,
University of Leicester, Leicester LE1 7RH, UK.
Contents
1
.
.
.
.
5
5
8
9
10
2
Stochastic Processe
Financial Mathematics II Name:
MA4072/7072/7418
Homework 7
Exercise 7.1. Suppose that the lifetime E of a machine is an exponential random variable with
mean 1/ . The machine is checked whether it is operating at regular intervals, namely, at times
T , 2T
Financial Mathematics II Name:
MA4072/7072/7418
Homework 6
Exercise 6.1. Consider an experiment that consists of counting the number of -particles given off
in a one-second interval by one gram of radioactive material. If we know from past experience that
Financial Mathematics II Name:
MA4072/7072/7418
Homework 5
We denote by cfw_Bt : t 0 a standard Brownian motion under the probability measure P and by
(Ft )t 0 its natural ltration, throughout.
Exercise 5.1. Let R. The Girsanov Theorem states that the sto
Financial Mathematics II Name:
MA4072/7072/7418
Homework 1
Exercise 1.1. Let A and B be independent events. Show that Ac and B are independent as well.
Deduce that Ac and Bc are also independent.
Solution: Clearly,
P (Ac B) = P (B \ cfw_A B)
= P(B) P(A B)
Financial Mathematics II Name:
MA4072/7072/7418
Homework 2
Throughout this homework, we let T 1 and denote by cfw_Bt : t [0, T ] a standard Brownian
motion and by (Ft )t [0,T ] its natural ltration.
Exercise 2.1.
(a)
(b)
Derive the condition expectations
Financial Mathematics II Name:
MA4072/7072/7418
Homework 1
Exercise 1.1. Let A and B be independent events. Show that Ac and B are independent as well.
Deduce that Ac and Bc are also independent.
Exercise 1.2. Let X be a discrete random variable. Show tha
Financial Mathematics II Name:
MA4072/7072/7418
Homework 3
We denote by cfw_Bt : t 0 a standard Brownian motion throughout.
Exercise 3.1.
(a)
(b)
Let f C2 (R; R). Write down the Ito formula as it applies to a function f (x) of a stochastic
process cfw_Xt
Financial Mathematics II Name:
MA4072/7072/7418
Homework 4
We denote by cfw_Bt : t 0 a standard Brownian motion and by (Ft )t 0 its natural ltration,
throughout.
Exercise 4.1. An analyst wishes to use a model which is based on Brownian motion, but which
d
MA7405
No. of Pages:
No. of Questions:
COURSE PROJECT
Subject
ACTUARIAL SCIENCE
Title of paper
MA7405 CONTINGENCIES
Time allowed
2
1
Deadline: 4pm, Friday the 11th May, 2012
Instructions to candidates
This project represents 30% of the module assessment.