Quiz 1
MATH 3281 3.00
Jan 12, 2015
Given name and surname:
Student No:
Signature:
INSTRUCTIONS:
1. Please write everything in ink.
2. This quiz is a ‘closed book’ test, duration 15 minutes.
3. Only non-programmable calculators are permitted.
4. The text has two pages, and it contains two questions. Read the
question carefully. Fill in answers in designated spaces. Your work
must justify the answer you give. Answers without supporting work
will not be given credit.
GOOD LUCK!
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Quiz 1
MATH 3281 3.00
Page 2 of 2
Question 1 Show that, given X ∋ X : Ω → [0, ∞), the functional
Hx [X] = E[X| X > x]
is an actuarial premium for all x ≥ 0.
Question 2 Consider a decision maker with the exponential utility function
u(x) = −e−5x , x ≥ 0.
The decision maker must choose between two financial prospects described by the r.v.’s
X ∽ N(5, 2) and Y ∽ N(6, 2.5). Which prospect will the decision maker choose?
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