1. If the demand for widgets is inelastic, then when the price of widgets increases, revenues will:

a. decrease

b. remain the same

c. increase

d. increase, unless there are substitutes for widgets

e. decrease because of the law of demand holds for widgets

2. Which of the following shifts the supply curve leftward?

a. An improvement in technology that decreases the cost of production.

b. An increase in the number of suppliers.

c. An anticipated drought that will make inputs more expensive.

d. A decrease in the wage rate.

3. Diminishing marginal rate of substitution necessarily implies that the marginal rate of

substitution

a. falls as one travels down (eastward) along an indifference curve.

b. falls as one travels up (westward) along an indifference curve.

c. stays the same as one travels up (westward) along an indifference curve.

d. decreases as the quantities of both goods increase.

e. we get less utility when we have higher incomes

4. Perfect complements will have indifference curves that are

a. concave to the origin.

b. vertical.

c. straight lines.

d. L-shaped.

e. horizontal.

In a traditional risk-neutral world with one risk factor, the Heath-Jarrow-Morton (HJM) model of the yield curve implies a generalised process for zero-coupon bond prices P(t, D) maturing at time / given by: dP(t, D) = r(D) P di + v(t, I, Q) P d.(() where r(1) is the short-term interest rate at time f and cde(?) is a standard Wiener process driving term structure movements. v(t, 7, Q) is the volatility of P, a generalised representation which also depends on Q, the collection of past and future interest rates and bond prices. (D) Define, in terms of P: (a) the forward rate /{{, 71: 7,) applying between times ], and 7, as seen at time : (b) the instantaneous forward rate F((, D) applying at time 7 as seen at time [2] (mi) Show that the process followed by the instantaneous forward rate F(1, D) is entirely determined by the volatility function v(t, 7, Q). [5] [Hint: Observe the process followed by ((1, 7, 7+AD) in the limit as A7-> 0.] iii) (a) Discuss the advantages and disadvantages of using the HIM model compared with other one-factor models of the yield curve such as the LIBOR Market Model and the Hull-White model. (b) Explain why it could be important to build models with more than one risk factor, and how suitable these models would be in multi-factor(10 points) You are given: Mortality Group Actual Claims Expected Claims A/E Male Nonsmoker 1,000 $30 120% Female Nonsmoker 350 945 90% Male Smoker 600 510 1 18% Female Smoker 50 55 91% Total 2,500 2.340 107% (a) (/ point) Compare and contrast the Limited Fluctuation and Buhlmann Empirical Bayesian credibility methods. (b) (/ point) Calculate the minimum number of claims required for full credibility under the Limited Fluctuation credibility method, assuming 95% confidence with a corresponding z-value of 1.96, and an error margin of 5%. Show all work. (c) (2 points) You have decided to combine smoker and nonsmoker experience for increased credibility. Evaluate the credibility of experience as measured by Limited Fluctuation for each gender and propose mortality adjustment factors as needed. Show all work. (d) (2 points) You are given key product differences summarized below: Current Product Repriced Product Target market Middle class High net worth Risk classes Smoker, Nonsmoker Smoker, Nonsmoker, Preferred Distribution Career agent Career agent, brokerage ART premium rates ART premium rates increase Premiums increase by 400% after by 150% after level term level term period period Describe the expected impact on the current mortality assumption for each of the differences above.(e) (4 points) The experience studies team is exploring mortality assumption adjustments for the following products: Product Description Deaths A/E Ratio Universal Life offered on Simplified Issue basis 200 200% Permanent life insurance sold to issue ages 18-25 600 105% Term life insurance for substandards 10,000 130% Permanent life insurance with 2 years of sales 20,000 60% (i) Evaluate the use of the Limited Fluctuation credibility method for each product, assuming the minimum number of deaths required for full credibility is 2,000 and the A/E ratios were developed using industry mortality rates. (ii) Recommend refinements to the mortality assumption for each product