Original PDF Flash format steven-shreve-on  


Steven Shreve On

Incisive Media presents
Steven Shreve on
Stochastic Calculus for Derivatives
Hong Kong
3 & 4 December 2009
This is a course on the fundamental
mathematical
concepts
underlying
modern quantitative finance. It assumes
delegates are familiar with differential
and integral calculus and probability
based on calculus and that they have
some knowledge of financial markets.
Course Highlights:
Systematic treatment of Brownian motion and Itô’s formula
Discussion of the assumptions behind risk-neutral pricing
Development of the connection between stochastic calculus and partial differential equations
Exposition of foreign exchange models
Derivation of the Heath-Jarrow-Morton no-arbitrage condition
Presentation of the fundamental idea behind LIBOR market models
Treatment of jump-diffusion models in option pricing and hedging
www.incisive-events.com/shreveasia
Working Knowledge:
Delegates should have a basic preparation in
differential and integral calculus and some
knowledge of probability
T h e c o u r s e
This unique course is specially designed
commendations from past delegates for
to equip quantitative risk managers
his methodology and style which allow
and specialist traders with a thorough
delegates to learn at a comfortable pace
understanding of stochastic calculus in
and pose questions to clarify difficult
derivatives and interest rate models. With
areas as and when necessary.
a clear and concise systematic approach,
All fundamental concepts from the theory
this intensive two-day course will train
of stochastic calculus will be illustrated
delegates in the application of continuous
by worked examples so that as well as
time financial mathematics, which
understanding highly technical articles,
underpin advanced finance.
delegates will learn how to manipulate
The expert course leader, Professor
theory and apply their knowledge in their
Steven E. Shreve, has received strong
own organizations.
Course Highlights:
Key Learning points
Systematic treatment of Brownian motion and
A sound knowledge of mathematical
Itô’s formula
terminology
Discussion of the assumptions behind risk-
An in-depth understanding of foreign exchange
neutral pricing
modeling
Development of the connection between
A thorough knowledge of the role of volatility
stochastic calculus and partial differential
in stochastic calculus
equations
A rigorous analysis of Brownian motion
Exposition of foreign exchange models
An examination of Heath-Jarrow-Morton model
Derivation of the Heath-Jarrow-Morton no-
An enhanced ability to read finance literature
arbitrage condition
Familiarity with forward measures
Presentation of the fundamental idea behind
Comprehension of Girsanov’s theorem and
LIBOR market models
risk-neutral measure
Treatment of jump-diffusion models in option
Insights into stochastic integrals and Itô’s
pricing and hedging
formula for multiple processes
A b o u t t h e I n s t r u c t o r
Steven Shreve
Stochastic Calculus’ and ‘Methods of Mathematical
Orion Hoch Professor
Finance’, advisory editor of the journal ‘Finance and
Department of Mathmatical Sciences
Stochastics’ and president of the Bachelier Finance
Carnegie Mellon University
Society.
Steven has supervised Ph.D. students in finance and
He has published over forty articles in scientific journals
teaches in the Carnegie Mellon master’s programme in
on stochastic control, including numerous articles on
computational finance, now in its fifteenth year, with
the application of these subjects to finance such as the
degrees offered in Pittsburgh and New York. He received
effect of transaction costs on option pricing, the effect
his M.Sc. in Electrical Engineering and his Ph.D. in
of unknown volatility on option prices, pricing and
Mathematics from the University of Illinois in 1977.
hedging of exotic options, convertible bonds and
Steven is the author of the book ‘Stochastic Calculus for
models of credit risk. Steven holds Carnegie Mellon
Finance’, co-author of the books ‘Brownian Motion and
University’s highest award for excellence in education.
“Outstanding course and job by Prof Shreve in
presenting the material. Truly excellent!”
“Excellent course! Second time around to this class
and both times my understanding of
stochastic calculus increased substantially”
Steven Shreve on Stochastic Calculus for Derivatives
Hong Kong 3 & 4 December
D a y o n e
D a y t w o
08.00
Registration and breakfast
08.00
Registration and breakfast
08.30
DEMYSTIFYING THE
08.30
CHANGE OF MEASURE
TERMINOLOGY
Girsanov’s Theorem
Sample spaces and random variables
Risk-neutral pricing
Fundamental Theorems of Asset
σ–algebrasandfiltrations
Adapted processes
Pricing
Conditional expectations
PARTIAL DIFFERENTIAL EQUATIONS
Martingales
Stochastic Differential Equations
Risk-neutral pricing
Feynman-Kac Theorem
10.00
Morning Break
10.00
Morning break
10.30
BROWNIAN MOTION
10.30
TERM STRUCTURE OF INTEREST
Construction as limit of scaled random
RATES
walks
Arbitrage problem with yield curve
Definition
evolution
Martingale property
Short-rate models
Quadratic variation – a measure of
Yield curve models (Heath-Jarrow-
volatility
Morton)
HJM under risk-neutral measure
ITÔ INTEGRALS
Construction for simple integrands
12.00
Lunch
Properties for simple integrands
13.20
CHANGE OF NUMERAIRE
Construction for general integrands
General theory
Example
Foreign exchange model
12.00
Lunch
14.20
Break
13.20
STOCHASTIC CALCULUS
14.40
FORWARD LIBOR MODEL
Itô formula for one process
Option pricing with random interest
Geometric Brownian motion
rate
14.20
Break
London interbank offer rate (LIBOR)
Black caplet formula
14.40
STOCHASTIC CALCULUS (cont.)
15.40
Break
Black-Scholes equation
Self-financing portfolios
16.00
INTRODUCTION TO JUMP
15.40
Break
PROCESSES
Poisson processes
16.00
STOCHASTIC CALCULUS (cont.)
Jump-diffusions and their integrals
Itô formula for multiple processes
Itô’s formula
Levy’s Theorem
Call on stock with fixed jump size
17.00
End of Day one
17.00
End of course
Who should attend?
RISK’S exclusive pre-course reading
This intensive two day training course will be of benefit to:
To maximise the value of the course and in addition to the
Quantitative researchers, Derivatives analysts, Quantitative
course documentation, before the course takes place Risk
analysts, Financial engineers, Project managers, Risk managers,
Training will send each delegate both volumes of Professor
Specialist dealers, Fund managers, Software developers, and
Shreve’s most recent book ‘Stochastic Calculus for Finance’,
Traders. It will also be of interest to students of stochastic
Springer-Verlag, 2004, along with a reading guide from
calculus and financial mathematics.
Professor Shreve.
www.incisive-events.com/shreveasia
Steven Shreve on
Stochastic Calculus for Derivatives
Hong Kong
3 & 4 December 2009
n
a
W
V
I
P
S
P
C
V
A
E
T
P
A
D
J
F
T
P
f
m
r
d
Y
n
a
A
b
H
m
e
c
l
I
l
T
e
G
e
A
a
a
i
l
P
P
M
E
O
D
O
o
e
E
I
I
o
o
R
T
l
r
a
s
P
L
o
e
n
a
/
s
a
a
R
i
A
S
D
P
B
S
L
e
m
c
u
x
e
R
T
i
N
d
k
c
v
V
s
s
D
a
R
E
u
r
T
A
I
R
t
n
c
e
P
I
O
L
P
T
T
E
a
i
m
r
b
v
m
r
/
R
o
t
A
e
A
e
f
H
Z
E
I
s
e
e
e
r
r
g
w
a
p
/
F
T
l
e
y
V
T
T
N
e
a
u
e
I
S
N
o
e
e
t
g
g
B
n
s
n
n
i
t
n
U
m
l
O
P
M
L
A
o
m
i
n
o
i
I
s
S
h
T
o
u
O
m
a
N
c
N
C
E
M
w
t
n
s
K
c
a
i
c
f
W
R
s
E
c
a
t
i
G
O
/
e
r
s
o
n
t
p
l
:
e
o
e
e
o
h
m
c
E
p
(
e
E
P
t
N
E
o
i
f
w
a
i
n
D
O
f
o
t
t
m
r
/
s
M
T
m
i
c
i
i
I
i
l
d
E
S
B
t
n
o
r
n
n
i
t
V
a
y
i
h
n
y
e
t
p
o
A
l
m
A
e
e
I
L
p
a
g
r
a
o
t
T
p
n
a
P
a
e
r
n
/
b
a
N
O
a
f
e
t
u
I
c
c
e
u
c
/
l
y
M
y
i
A
O
l
c
e
C
y
k
e
i
a
a
b
r
c
t
c
d
h
r
G
N
K
,
.
o
B
t
c
c
C
l
e
i
p
o
)
m
h
e
t
e
i
w
B
n
E
e
q
h
h
s
e
C
c
e
n
s
M
D
e
h
l
u
.
a
y
t
u
q
f
q
S
i
n
a
R
e
u
o
l
A
y
e
o
u
s
n
c
u
P
r
e
k
d
o
i
D
u
t
s
/
g
S
a
e
M
e
e
i
a
l
o
p
I
e
T
q
o
u
a
s
r
e
c
n
s
V
A
u
y
n
e
W
i
d
A
o
d
,
A
s
p
s
r
e
L
a
l
b
i
t
U
c
T
d
a
s
S
b
n
r
V
3
u
p
S
n
r
r
M
M
d
e
t
y
l
e
a
.
e
a
h
e
T
N
o
e
S
0
a
e
t
n
h
o
k
E
i
o
d
/
F
o
t
s
A
A
t
b
$
t
n
i
t
a
o
r
f
l
a
S
e
s
t
P
:
s
2
1
e
c
A
G
g
S
E
l
a
t
f
e
I
a
s
e
d
4
5
o
a
u
i
T
S
i
a
n
x
t
B
f
l
p
r
r
n
E
a
T
t
s
c
c
,
6
%
d
d
o
o
i
t
l
s
h
u
R
u
7
f
s
r
R
R
a
m
5
i
b
p
i
v
e
n
a
f
9
2
a
x
a
6
f
C
O
I
y
c
n
b
n
e
e
c
h
e
0
t
n
u
9
A
o
e
c
e
d
t
0
s
8
r
l
F
o
r
e
e
1
I
R
i
o
f
i
m
a
n
n
s
t
9
w
b
h
e
n
s
w
h
a
p
d
6
D
i
a
e
h
5
d
t
s
v
i
n
l
s
e
r
n
r
u
c
e
k
e
f
e
t
e
F
u
T
F
C
C
C
L
w
b
i
n
r
e
a
e
f
t
o
n
o
F
R
A
o
O
I
O
A
l
d
r
e
r
T
B
i
r
t
a
m
n
t
A
i
A
X
S
h
o
P
U
n
c
n
Y
M
k
f
s
e
h
i
u
I
T
e
u
o
h
i
D
o
s
l
M
N
N
n
b
r
a
f
f
m
a
m
a
P
m
N
n
m
g
y
o
i
s
n
I
T
l
A
i
e
b
N
s
e
s
S
b
r
p
o
b
E
R
A
o
c
N
f
G
y
h
w
o
n
r
c
s
a
e
u
e
X
Y
M
i
Y
i
e
.
n
v
o
r
t
n
i
a
m
t
s
A
o
e
r
r
M
P
i
e
E
g
h
U
n
e
l
u
,
w
V
3
u
l
p
A
a
L
y
e
s
P
S
E
1
n
s
a
a
N
b
c
t
o
h
e
i
u
d
c
u
e
s
n
y
$
t
A
o
o
.
n
e
b
r
r
O
e
2
1
t
E
m
G
o
m
I
e
n
c
.
l
d
a
U
6
0
c
P
l
e
D
V
i
E
r
s
k
p
a
o
e
l
R
v
6
%
t
l
o
m
n
R
e
I
I
a
r
d
h
w
N
S
o
n
d
a
i
a
t
9
e
i
A
i
e
t
i
l
2
a
s
E
n
n
e
a
r
c
a
m
h
s
b
0
t
e
e
m
b
a
R
g
t
t
a
o
y
h
r
l
e
d
0
s
e
s
S
L
o
a
t
i
9
a
n
r
b
t
t
u
t
p
d
r
t
i
C
e
m
s
d
h
r
w
e
e
t
e
p
t
L
a
.
i
e
-
a
c
t
u
e
s
a
h
t
U
i
o
m
y
p
l
e
n
s
u
e
A
s
B
c
m
r
o
,
r
e
o
r
o
s
o
e
c
o
f
v
f
e
D
E
n
u
n
e
r
e
t
e
s
c
e
l
n
e
y
e
A
X
t
s
f
o
r
r
.
s
e
l
r
t
v
:
i
T
P
s
P
l
a
y
o
n
e
P
v
E
I
e
l
d
e
o
w
3
U
a
n
l
e
R
i
e
a
u
n
1
P
m
H
w
a
d
Y
s
r
u
g
S
e
r
s
r
p
K
a
e
e
$
O
i
o
e
D
c
c
g
t
n
a
r
o
h
d
k
w
A
–
i
2
c
e
n
m
s
e
i
d
n
8
r
T
4216/09
t
y
t
r
g
i
t
E
p
p
o
a
9
d
e
l
r
u
2
e
d
:
e
t
o
i
r
9
0
l
a
y
t
o
v
e
e
n
i
y
o
s
0
g
s
u
t
w
i
a
h
o
r
9
t
f
e
i
n
e
o
t
h
a
r
l
*
P
a
P
M
d
I
M
I
s
i
B
m
b
I
u
t
v
b
t
D
a
t
C
I
W
n
n
n
n
F
l
n
l
o
e
h
e
e
o
d
a
c
a
c
f
y
r
s
e
o
e
l
h
n
w
c
V
r
a
o
c
o
e
i
i
w
a
s
n
l
a
w
P
V
r
a
i
n
i
s
i
i
s
v
r
i
s
F
s
l
o
l
r
a
i
i
i
e
l
c
o
o
a
s
r
c
a
o
i
e
n
d
u
e
a
e
v
v
c
m
i
l
c
i
a
s
r
n
h
r
t
n
t
e
t
g
l
e
l
e
e
e
g
u
r
i
e
l
c
s
G
S
w
s
n
B
B
B
B
A
1
2
I
B
e
y
i
n
i
m
g
a
e
v
i
w
e
i
s
r
x
a
i
e
n
s
r
w
i
t
w
s
s
s
r
o
i
i
l
e
n
e
e
t
e
c
n
t
i
M
M
c
i
t
c
e
n
m
r
t
w
l
r
p
w
f
t
n
e
o
y
y
y
d
8
0
e
a
a
m
i
w
o
e
a
t
o
k
P
s
o
.
g
h
M
g
r
o
t
c
y
P
t
o
e
h
e
e
n
r
r
o
m
n
I
e
e
e
t
:
w
s
u
f
e
h
i
d
h
h
i
e
n
t
t
r
l
k
i
v
e
.
r
h
o
m
/
o
e
R
u
i
e
d
n
j
h
o
c
m
f
o
t
i
r
.
e
e
o
o
i
o
i
c
o
e
g
c
a
u
c
v
:
c
s
y
a
a
n
n
h
l
o
u
i
n
i
e
,
e
T
o
n
d
i
i
c
n
e
e
f
t
H
F
i
s
m
n
k
a
s
m
b
o
a
f
l
r
n
n
h
m
b
i
s
c
:
a
p
-
e
,
k
i
c
i
a
i
c
I
i
e
r
w
e
v
e
n
p
u
e
w
t
o
r
r
i
c
i
w
e
i
r
n
v
o
A
.
u
e
e
a
s
a
r
c
i
a
i
d
t
e
f
W
i
i
n
m
x
l
r
T
v
n
r
e
g
i
e
a
l
e
a
o
i
r
s
e
o
s
p
r
n
t
a
e
l
a
g
S
c
f
a
r
e
t
,
n
F
e
o
a
r
e
a
s
D
s
e
o
a
r
a
l
c
+
c
o
e
i
s
c
e
n
h
r
i
a
b
t
t
a
o
t
e
f
v
i
n
a
+
l
i
t
o
w
l
i
e
v
e
a
l
p
t
e
.
d
i
.
i
e
s
e
b
w
n
r
n
u
r
g
n
w
i
G
,
s
o
s
e
d
s
t
h
o
F
a
v
P
a
*
l
a
a
a
d
t
e
r
o
h
n
f
s
e
l
i
y
F
(
i
i
n
f
a
i
n
a
r
i
e
t
e
l
t
i
e
s
t
n
A
n
/
a
t
a
o
a
e
d
i
g
l
o
c
i
h
h
i
p
v
w
c
y
f
x
i
v
n
a
e
c
l
y
m
e
l
i
c
s
r
-
v
i
l
(
8
,
u
C
e
i
o
n
8
l
r
l
c
i
a
l
o
p
o
l
e
s
o
u
S
s
p
a
i
x
e
(
a
l
t
r
a
d
p
s
a
m
e
c
e
o
o
e
e
c
5
H
r
n
o
u
t
v
v
e
5
t
r
a
u
u
y
r
e
r
n
l
i
e
p
r
e
c
d
m
w
l
a
w
e
h
d
o
s
y
P
e
e
c
t
r
v
r
f
m
c
r
e
e
a
e
s
t
o
n
r
s
e
f
u
u
r
M
2
n
o
t
s
d
u
e
2
o
R
2
n
s
i
o
a
c
l
e
e
i
n
e
o
u
o
a
c
o
m
t
1
n
n
-
c
d
h
m
l
t
a
E
n
v
i
e
b
o
i
o
r
i
b
d
n
c
t
b
u
k
h
.
p
n
w
n
f
)
e
n
0
t
a
r
e
)
n
,
f
o
c
e
e
h
n
e
o
r
m
e
t
i
t
l
e
i
n
a
a
W
r
o
e
e
.
o
s
i
e
s
a
%
n
a
t
t
3
t
s
r
y
r
d
c
n
d
o
v
s
I
s
f
m
n
e
e
f
u
a
i
o
I
u
t
o
t
r
h
l
s
g
s
e
y
d
h
s
D
s
w
@
3
g
A
i
r
a
a
4
e
n
n
r
u
e
i
c
i
r
l
i
f
r
a
n
i
.
c
e
e
o
i
n
a
i
.
a
i
4
n
m
I
h
.
r
v
o
l
l
m
a
S
t
i
s
n
y
i
m
t
:
f
j
o
g
u
n
e
d
n
m
e
a
e
m
n
d
I
f
t
u
n
e
m
i
o
v
s
p
t
d
o
a
r
f
e
r
c
n
g
m
f
a
i
c
a
n
w
i
n
1
K
d
d
l
n
T
1
,
m
P
r
a
L
i
r
s
o
s
y
i
t
r
e
e
e
e
t
l
i
c
i
a
a
r
s
g
r
t
t
M
o
l
h
l
e
r
t
l
.
t
e
i
n
r
v
d
w
t
n
k
e
e
i
h
i
t
n
d
i
i
e
g
c
m
.
c
1
o
c
1
u
n
b
n
v
t
i
,
d
a
s
e
f
i
s
f
e
a
o
o
i
a
r
c
o
e
r
v
s
s
g
I
y
n
n
r
e
c
e
d
t
a
o
e
n
i
n
i
e
O
d
s
e
t
a
e
t
o
e
h
t
m
u
.
e
t
a
c
M
u
r
n
e
i
o
s
4
r
b
l
b
4
g
a
d
d
c
n
p
t
w
i
c
r
i
d
t
o
c
d
i
f
s
r
a
a
r
e
e
d
s
e
e
r
t
t
t
a
u
r
c
i
v
8
l
A
8
l
i
t
a
e
t
a
i
e
d
i
c
o
a
i
r
t
y
C
v
h
r
d
e
e
i
n
t
n
o
t
v
r
e
d
d
o
t
h
a
b
n
i
s
i
n
s
e
8
t
s
d
p
v
i
d
n
t
h
k
o
w
a
e
e
e
o
n
i
1
y
h
e
i
o
e
e
m
t
l
e
i
b
a
i
u
e
f
e
i
r
t
u
l
s
e
i
a
o
o
s
d
h
i
c
M
d
r
f
f
t
m
y
a
n
e
e
t
l
l
.
l
s
l
e
h
o
i
s
e
t
f
t
i
o
e
v
m
8
m
R
1
C
i
u
,
s
o
t
r
e
t
e
h
m
v
p
I
s
e
f
l
a
t
e
e
c
f
f
e
t
s
n
a
o
u
u
l
i
/
e
a
a
f
e
u
n
d
a
c
)
e
.
.
r
e
:
f
i
m
e
e
d
t
a
n
s
a
o
y
r
n
s
i
r
e
r
n
r
w
,
o
g
n
E
d
i
l
t
e
P
-
a
s
i
s
e
r
t
a
t
l
o
g
w
e
p
d
r
c
s
i
e
l
i
i
l
d
f
i
o
n
e
o
u
o
f
s
o
h
n
t
s
i
i
r
e
d
n
i
l
g
o
a
h
e
l
s
h
n
l
h
t
l
d
o
e
n
y
s
w
y
a
r
o
n
t
d
e
e
c
b
e
t
a
v
i
L
s
t
G
t
t
a
t
d
o
x
s
u
r
r
a
f
o
t
i
o
D
t
e
n
n
n
a
e
s
e
i
t
e
r
r
o
n
u
t
o
d
e
o
n
n
a
o
n
e
r
t
r
.
e
d
h
h
f
e
b
c
m
a
t
o
g
n
e
s
e
i
a
e
d
r
i
b
t
n
w
u
t
c
t
m
o
n
r
o
r
h
o
r
i
t
t
e
r
s
s
n
u
n
c
a
,
.
e
a
c
e
a
y
v
e
e
e
t
f
v
a
m
o
e
a
n
o
w
c
t
s
d
u
w
a
e
o
p
t
o
t
I
,
i
a
i
b
c
l
e
s
y
a
f
t
e
w
l
k
p
g
r
t
s
e
a
l
e
n
i
o
m
i
i
o
o
a
m
i
n
i
v
i
v
i
n
o
i
h
u
v
d
n
d
s
m
o
S
i
a
l
a
l
t
r
c
e
u
e
l
a
s
a
e
c
i
e
g
n
s
b
n
r
e
f
e
c
a
.
n
s
l
s
o
t
n
h
t
s
a
,
s
t
n
n
r
f
o
g
a
c
i
a
e
t
o
o
c
t
,
T
–
m
u
w
y
t
i
n
t
o
n
d
o
b
o
y
n
I
v
a
u
e
o
s
o
w
a
l
b
o
n
n
l
e
u
a
y
i
s
n
i
t
i
l
l
c
f
i
n
e
n
l
i
i
y
n
u
o
c
i
y
r
.
p
b
c
f
t
e
t
c
r
d
w
g
a
s
a
x
e
a
e
y
e
e
t
o
o
m
i
s
d
e
o
s
m
w
e
m
b
e
c
b
i
i
a
l
s
r
r
h
t
E
f
m
u
e
f
,
o
e
a
n
i
l
o
s
e
o
v
t
a
c
o
t
t
n
a
/
n
h
f
h
.
s
e
e
u
:
i
u
e
e
r
o
r
t
n
w
c
i
v
n
s
c
t
e
c
i
u
s
a
d
s
c
i
a
o
s
s
R
d
t
e
M
o
e
a
o
t
g
c
t
o
o
e
i
a
t
u
i
n
n
u
h
w
n
s
p
I
n
r
b
i
s
u
h
o
u
e
t
y
d
r
,
n
e
c
l
d
r
a
c
i
t
p
e
t
r
d
o
i
l
h
r
o
l
w
l
c
o
c
r
r
r
e
.
z
o
v
o
t
l
i
o
i
e
h
e
r
e
a
e
f
i
i
c
r
f
n
s
o
l
h
s
l
©
u
f
e
t
m
n
i
a
p
r
*
c
r
e
h
e
o
i
d
a
h
i
n
o
e
s
v
r
o
r
.
t
u
v
s
s
d
r
r
e
w
c
t
e
e
o
e
r
s
t
e
i
I
s
o
o
r
d
t
b
h
A
o
n
r
e
r
e
d
p
d
l
i
,
a
r
M
n
c
t
t
e
m
t
e
r
l
s
e
e
s
h
i
a
i
u
l
a
c
v
e
p
n
r
d
s
i
i
s
a
o
a
e
u
s
s
e
r
c
a
.
t
k
a
l
l
d
v
a
i
r
/
c
e
e
e
w
c
t
n
a
m
d
b
v
e
m
b
s
r
i
n
e
o
o
e
e
s
v
n
a
t
t
d
l
t
m
x
s
h
a
s
h
i
i
i
s
e
t
d
d
t
a
o
a
t
h
a
c
e
i
n
n
n
e
e
i
h
c
M
m
i
s
g
r
i
t
e
e
e
o
a
/
l
b
u
d
y
r
d
f
t
y
o
i
n
n
e
e
u
i
e
r
o
o
o
r
s
t
v
c
e
p
s
e
s
a
i
E
l
s
r
u
f
t
u
r
t
a
t
e
e
d
e
o
r
k
i
n
f
h
o
i
s
t
v
e
m
e
o
r
u
e
p
r
d
a
p
e
f
v
d
g
a
e
m
e
v
r
d
u
r
r
p
p
.
y
a
n
e
e
i
p
a
v
o
a
t
u
r
t
c
l
c
r
n
r
a
i
n
i
r
c
i
t
o
f
i
o
c
h
t
a
e
o
o
s
l
i
e
g
t
w
h
f
l
t
e
t
a
h
n
d
n
p
t
g
h
n
s
e
t
e
b
t
e
s
n
f
e
h
a
r
t
r
a
e
r
e
t
i
e
t
o
r
o
.
f
a
f
o
f
c
s
r
u
r
t
e
i
x
I
o
n
t
t
e
y
r
n
f
t
.
f
t
e
i
i
e
m
d
u
b
n
g
i
s
g
r
o
s
y
r
e
c
h
n
:
o
e
e
t
u