Problem 10.4. Source: Sample STAM Problem #280. A compound Poisson claim distribution has the parameter A equal to 5 and individual claim amounts X distributed as follows: px (5)= 0.6 and px (9) = 0.4. What is the expected cost of an aggregate stop-loss insurance subject to a deductible of 5?
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- Problem 1. Let x be the level of precaution, w=16 is the marginal cost of precaution, p(x)=1/x is the probability of an accident, and A=10,000 is the cost of an accident. Find the efficient precaution level.Working problem 4.12: If the event is a number '5' tuming in rolling a die, simulate rolling a die for 1000 times with increments of 100 and explain how the law of large numbers will prevail. Working problem 4.13 : The data in the Table below was taken from the U.S. Census Bureau report titled "HINC-01. Selected Characteristics of Households, by Total Money Income in 2005" (http://www.census.gov/hhes www/cpstables/032010/hhinc/new01 001.htm) Income Under $20,000 $20,000 to < $40.00O $40,000 to < $60.00O S60,000 to < $80,000 $80,000 to < $100,000 Above $100,000 Households (thousands) 24,559 26,904 20.026 14,535 9,362 7,813 If a U.S. family is selected at random, Determine (a) The probability that the family selected has an annual income of less than $40,000 (b) The probability that the family selected has an annual income of $40,000 to less than $80,000 (c) The probability that the family selected has an annual income of more than $100,000 29(c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. Week 1 2 3 4 5 6 Time Series Value 18 11 15 10 17 12 18 Forecast 16.6 16.28 15.024 15.419 X Compute MSE. (Round your answer to two decimal places.) MSE = 21.40 X What is the forecast for week 7? (Round your answer to two decimal places.) 14.74
- PROBLEM 16-12 Financial Ratios for Common Stockholders [L02] Refer to the financial statements and other data in Problem 16-11. Assume that you have just inherited several hundred shares of Modem Building Supply stock. Not being acquainted with the company, you decide to do some analytical work before making a decision about whether to retain or sell the stock you have inherited. Required: 1. You decide first to assess the well-being of the common stockholders. For both this year and last year, compute the following: a. The earnings per share. b. The dividend yield ratio for common stock. The company's common stock is currently sell- C. ing for $45 per share; last year it sold for $36 per share. The dividend payout ratio for common stock. d. The price-earnings ratio. How do investors regard Modern Building Supply as compared to other companies in the industry? Explain e. The book value per share of common stock. Does the difference between market value and book value suggest that the…Need assistance with question 2 iv, v. I already got help with i, ii, iiiSolve this problem
- A large manufacturer purchases an identical component from three independent suppliers that differ in unit price and quantity supplied. The relevant data for 2012 and 2014 are given here. Unit Price ($) Supplier Quantity (2012) 2012 2014 A 150 5.95 6.50 B 100 5.60 5.95 160 5.50 6.70 (a) Compute the price relatives (index number) for each of the component suppliers separately using 2012 as the base year. (Round your answers to the nearest integer.) Item Price Relative A В Compare the price increases by the suppliers over the two-year period. --Select--- v prices increased, with the greatest price relative being from supplier -Select--- v and the smallest price relative being from supplier -Select--- v (b) Compute an unweighted aggregate price index for the component part in 2014. (Round your answer to the nearest integer.) I 2014 = (c) Compute a 2014 weighted aggregate price index for the component part. (Round your answer to the nearest integer.) I2014 - What is the interpretation of…17. A risk manager would like to simulate the price of a stock using the discretized GBM, where St+At = St + µS{At+√ã$£€ where μ and o denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.5% and the weekly volatility is 4%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of μ? (a) = 26.4% (b) û = 30.16% (c) û = 4.5% (d) û = 17.94% 18. Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift μ = 0.01 and an annual volatility of o= 0.25. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GBM, the future price at T, i.e. ST, given today's spot price, St, is with TT-t and €~ = (a) 21.51% (b) 35.48% (c) 51.1% (d) 30.47% ST= St x exp (μ x exp [(μ-27 ) XT + √F X 0 Xe] N (0, 1).3. Suppose Par = $10,000,000; PO = $7,500,000; T = 3; d = 0.006; m = 0.7 and π = 0.5. Then what is the expected zero rate? * O a. 9.97% pa. O b. 8.92% pa. O c. 7.92% pa. O d. 9.64% pa. O e. 9.92% pa.
- The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-6. what is find level Curve by 3upposing Jevet Curve? if $(z)= Z+ 4 . Z-4 %3D mecessary Subsitution.Question 6 Having studied Fixed Income Securities, you are now working as an analyst for a well known bond fund. Your manager asks you to replicate the JP Morgan T-Bond Index using a tracking error minimization approach. You are to replicate this index as closely as possible using a medium duration Treasury bond (M-BOND) and a long duration Treasury bond (L-BOND). These expire in approximately 7.15 years’ and 29.25 years’ time respectively. The following variance-covariance matrix, based on daily returns over the preceding six months, is given to you to use in your replication: Note: As usual, variances are given on the diagonal, e.g. the variance of M-BOND is 0.0042%. As usual, covariances appear in the non-diagonal elements, e.g. the covariance of M-BOND and L-BOND is 0.0057%. (a) Suppose the optimal weights for M-BOND and L-BOND are 0.7 and 0.3. Calculate the expected tracking error of the portfolio and explain how you interpret this number. (b) Calculate the correlation matrix…