PRMIA 8007 Exam : Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Jul 26, 2026
  • Q & A: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Stochastic Processes and Time Series- Time series analysis
  • 1. Autocorrelation and stationarity
    • 2. AR, MA, and ARMA models
      - Stochastic processes basics
      • 1. Markov processes
        • 2. Brownian motion (introductory level)
          Simulation and Numerical Methods- Monte Carlo simulation
          • 1. Risk distribution simulation
            • 2. Random number generation
              Risk Measurement Techniques- Volatility and correlation
              • 1. Correlation estimation techniques
                • 2. Variance-covariance methods
                  - Value at Risk (VaR)
                  • 1. Parametric and non-parametric VaR
                    • 2. Historical simulation approach
                      Probability and Statistics Foundations- Random variables and probability distributions
                      • 1. Expectation, variance, and moments
                        • 2. Discrete and continuous distributions
                          - Statistical inference
                          • 1. Estimation theory
                            • 2. Confidence intervals and hypothesis testing

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

                              1. The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:

                              A) 128
                              B) 20
                              C) 12
                              D) Infinity


                              2. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

                              A) E(exp(X)) = 0.6065
                              B) E(exp(X)) = 2.7183
                              C) E(exp(X)) = 1.6487
                              D) E(exp(X)) = 1


                              3. Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses...

                              A) One dependent variable, one independent variable, many error variables
                              B) One dependent variable, many independent variables, one error variable
                              C) Many dependent variables, many independent variables, many error variables
                              D) Many dependent variables, one independent variable, one error variable


                              4. There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds.
                              Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

                              A) None of these
                              B) 0.3
                              C) 0.6
                              D) 0.5


                              5. Variance reduction is:

                              A) A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
                              B) A method for reducing the number of simulations required in a Monte Carlo simulation
                              C) A numerical method for finding the variance of the underlying that is implicit in a market price of an option
                              D) A technique that is applied in regression models to improve the accuracy of the coefficient estimates


                              Solutions:

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

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