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

1. Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

A) f(dg/dy)
B) f'(g(x,y))
C) f(g(x,y)) dg/dy
D) f'(g(x,y)) dg/dy

2. Find the first-order Taylor approximation p(x) for the function: at the point .

A) x+1
B) x-1
C) -x+1
D) -x

3. The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A) x = 0, y = 20
B) x = 5, y = 0
C) x = -1, y = 0
D) None of the above

4. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5288
B) 0.5286
C) 0.5290
D) 0.5292

5. What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

A) 1 048 595
B) 2 097 170
C) 1 048 574
D) 2 097 172

Solutions: