April 2011
Intermediate to advanced
328 pages
9h 5m
English
Content preview from Risk Analysis in Finance and Insurance, 2nd Edition
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Analysis of Risks: Continuous Time Models 131
Similarly to Case 1,
x
0
= S
0
Φ(d
+
) − Φ
σ
√
T −
b
1
√
T
+Φ
σ
√
T −
b
2
√
T
−Ke
−rT
Φ(d
−
) − Φ
−
b
1
√
T
+Φ
−
b
2
√
T
.
The problem of quantile hedging can be considered from a different per-
spective: the pay-off function f
T
can be interpreted as an investment objective
for a given investment period [0,T]. Then the terminal value X
π
T
of an invest-
ment strategy π should be “close enough” to the objective in some probabilistic
sense.
If the measure of closedness is chosen to be E
|X
π
T
−f
T
|
2
, then we arrive at
the notion of the mean-variance hedging. Alternatively, we can use the notion
of a loss function l : R
+
→ R
+
, which is commonly ...
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