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

  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Sep 15, 2026
  • Q & A: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

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

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

                              Question #1

                              The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

                              • A. f has necessarily a maximum at this point
                              • B. f has necessarily neither a minimum nor a maximum at this point
                              • C. f might have either a minimum or a maximum or neither of them at this point
                              • D. f has necessarily a minimum at this point
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Question #2

                              Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

                              • A. 1.638
                              • B. 0.377
                              • C. 2.362
                              • D. 1.623
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

                              Question #3

                              I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

                              • A. 2.50%
                              • B. -2.50%
                              • C. 5%
                              • D. -5%
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

                              Question #4

                              Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

                              • A. the PDF is non-negative.
                              • B. the CDF approaches 1 as its argument approaches infinity.
                              • C. the definite integral of the CDF from minus infinity to plus infinity is undefined.
                              • D. the definite integral of the PDF from minus infinity to plus infinity is zero.
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

                              Question #5

                              Which of the following statements is not correct?

                              • A. Every linear function is also a quadratic function.
                              • B. For finite and small domains, the action of a function may be specified by a list.
                              • C. A function is defined by its domain together with its action.
                              • D. A function is a rule that assigns to every value x at least one value of y.
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

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