StatRisk solution homework assignment 6
Problem 10.1
a) By Theorem 10.4(b),
function, hence
g
d
n ) Y Nd (0, ). Also g(y) = y0 1 y is a continuous
n(
d
n ) = n(
n )0 1 (
n ) Y0 1 Y 2 (d),
n(
where the last part follows from Problem 6.1.
b) Now let g()
StatRisk solution homework assignment 2
Problem 3.5 As in Problem 3.3 we can ignore the multiplicative constants. Let h(x) =
log x + log f (x).
a) Here
h(x) = c + log x
1
(x )2 as x ,
2 2
so the N (, 2 ) distribution is not heavy tailed.
b) Here
h(x) =
StatRisk solution homework assignment 8
Also here my results are based on the older data.
Problem 12.2 The following program worked
% Program to make Q-Q plots and Kolmogorov-Smirnov tests
global x alpha beta theta const q ind;
x=-usindexwld(:,2);
x=x(x>0
StatRisk homework assignment 7
Due November 25
Problems are taken from the notes.
Chapter 11: Problems 11.1d, 11.3 and 11.6.
Chapter 12: Problems 12.1.
For Problem 12.1 it is sufficient to do the analysis for the Pareto and lognormal distributions. As a h
StatRisk homework assignment 3, due October 21
Problems are taken from the notes.
Chapter 5: Problems 5.1, 5.2, 5.3, 5.5 and 5.7.
Chapter 6: Problems 6.1, 6.2 and 6.3.
1
StatRisk solution homework assignment 1
Problem 2.1 Here
FX|a<Xb (x) =
P (X x, a < X b)
F (mincfw_x, b) F (mincfw_x, a)
=
.
P (a < X b)
F (b) F (a)
Problem 2.3 Let X = 1 if the stock defaults and X = 0 otherwise. Let W = i if stock i is
picked.
a) Here
P
StatRisk homework assignment 4
Due October 28
Problems are taken from the notes.
Chapter 7: Problems 7.1, 7.2, 7.3 and 7.4.
Extra Problem 1:
Assume you have n portfolios, and let Xi be the number of losses on portfolio i. It is assumed
that given W = w, X
StatRisk homework assignment 5
Due November 11
Problems are taken from the notes.
Chapter 8: Problems 8.1, 8.2, 8.3 and 8.5.
Chapter 9: Problems 9.1, 9.2 and 9.3.
1
StatRisk homework assignment 1, due October 6
Problems are taken from the notes.
Chapter 1: Problem 1.1.
Chapter 2: Problems 2.1, 2.3 and 2.4.
Extra problem 1, Chapter 2
Let the time until a claim N is paid have the geometric distribution
P (N = n) = p(1