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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Probability Theory | 25% | - Basic probability concepts
|
| Calculus and Functions | 20% | - Multivariable calculus
|
| Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Time value of money - Basics of risk modeling |
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by
- A. F(x)G(x)
- B. F(x)g(x) - F(x)g'(x)dx
- C. f(x)G(x) - F(x)g'(x)dx
- D. F(x)g(x) + f(x)G(x)
Correct Answer: B 🗳️
Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?
- A. N'(x) 0 as x
- B. N'(0) 0
- C. N(x) 0 as x
- D. N(0) = 0.5
Correct Answer: C 🗳️
Variance reduction is:
- A. A method for reducing the number of simulations required in a Monte Carlo simulation
- B. A technique that is applied in regression models to improve the accuracy of the coefficient estimates
- C. A numerical method for finding the variance of the underlying that is implicit in a market price of an option
- D. A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
Correct Answer: A 🗳️
A 95% confidence interval for a parameter estimate can be interpreted as follows:
- A. The probability that the estimated value of the parameter is outside this interval is 95%.
- B. The probability that the real value of the parameter is outside this interval is 95%.
- C. The probability that the real value of the parameter is within this interval is 95%.
- D. The probability that the estimated value of the parameter is within this interval is 95%.
Correct Answer: C 🗳️
Maximum likelihood estimation is a method for:
- A. Solving a portfolio optimization problem
- B. Finding parameter estimates of a given density function
- C. Estimating the solution of a partial differential equation
- D. Estimating the implied volatility of a simple European option
Correct Answer: B 🗳️
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