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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. The gradient of a smooth function is

A) a matrix containing the function's second partial derivatives
B) infinite at a maximum point
C) matrix of second partial derivatives of a function
D) a vector that shows the direction of fastest change of a function


2. If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A) 3/4
B) None of these
C) 12/29
D) 37/45


3. What is a Hessian?

A) The vector of partial derivatives of a contingent claim
B) Correlation matrix of market indices
C) A matrix of second derivatives of a function
D) The point at which a minimum of a multidimensional function is achieved


4. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A) 1 / (x+y)
B) (x + y) / (x+y)
C) ln(x+y) x + ln(x+y) y
D) -x/(x+y) - y/(x+y)


5. You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A) a continuously-compounded rate of 4%
B) a quarterly-compounded rate of 4.1%
C) a lump-sum payment of $22 500 on maturity (in five years)
D) an annually compounded rate of 4.15%


Solutions:

Question # 1
Answer: D
Question # 2
Answer: D
Question # 3
Answer: C
Question # 4
Answer: B
Question # 5
Answer: B

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