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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Numerical Methods & Financial Mathematics | 15% | - Time value of money - Basics of risk modeling - Root finding and approximation |
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Probability Theory | 25% | - Basic probability concepts
|
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Calculus and Functions | 20% | - Single-variable calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. An asset price S is lognormally distributed if:
A) ln(1+dS/S) is normally distributed
B) ln(dS/S) is normally distributed
C) 1/S is normally distributed
D) the change in price (dS) is normally distributed
2. Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?
A) 1.623
B) 1.638
C) 2.362
D) 0.377
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) None of the above
B) x = -1, y = 0
C) x = 5, y = 0
D) x = 0, y = 20
4. Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?
A) 2/5 and 1/2
B) 9/25 and 12/25
C) 2/5 and 3/5
D) 1/3 and 8/17
5. Find the roots, if they exist in the real numbers, of the quadratic equation
A) -4 and 2
B) 1 and 0
C) No real roots
D) 4 and -2
Solutions:
| Question # 1 Answer: A | Question # 2 Answer: B | Question # 3 Answer: D | Question # 4 Answer: B | Question # 5 Answer: C |




