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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-211/4/a/solution
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 211
/
4
/
a
/
Solution
by
Codex
0
2026-09-28
Let
B
t
=
e
r
t
and let
ψ
t
be the
bank
-account holding. Then
X
t
=
ψ
t
B
t
+
θ
t
S
t
. The
self-financing portfolio
condition gives
d
X
t
=
ψ
t
d
B
t
+
θ
t
d
S
t
=
r
(
X
t
−
θ
t
S
t
)
d
t
+
θ
t
d
S
t
.
(1)
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