Value-at-Risk Theory and Practice

The first advanced book on value-at-risk

Chapter 3, Page 143
Exercise 34

Derive formulas [3.114] and [3.115].

Solution

a. We apply [3.4], [3.113] and use the fact that an integral of a sum is a sum of integrals:

[s1]

[s2]
[s3]
[s4]
[s5]
[s6]

b. We apply the result of Exercise 3.15, we obtain

[s7]

[s8]
[s9]
[s10]
[s11]
[s12]
[s13]
[s14]

The second representation indicated in [3.115] is obtained with a second application of the result from Exercise 3.15.

 

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